I'm a real precisionist. I don't even think that's a word. Anyway... I'm the sort of person who will sit in a movie and point out the mistakes. I found about 15 in my first viewing of PoA.
So this is a page to put anything that has been found. Difference between the books and the films are NOT mistakes, but both continuity mistakes and book inconsistencies are! So if you've noticed one that isn't here, let me know!
Thanks to MovieMistakes.com for some of these.

PHILOSOPHER'S STONE book
» We know that Harry's birthday is on July 31 because that is the same day as the break-in at Gringotts. From CoS we know Nearly Headless Nick's 500th Death Day Party was on 10/31/1992. Doing the math, we know that Harry's 11th Birthday was 07/31/1991. In PS, Harry says his birthday is on a Tuesday, the day after Dudley's favorite TV show (The Great Humberto). The mistake is that July 31, 1991 fell on a Wednesday, not a Tuesday like the book said.
» On page 133, 4th paragraph, it says that Hermione lent Harry Quidditch through the ages: "She had also lent him Quidditch Through the Ages, which turned out to be a very interesting read." On page 46 paragraph 3 of QTtA, it says "The most successful Japanese team, The Toyohashi Tengu, narrowly missed a win over Lithuania's Gorodok gargoyles in 1994." However, Harry borrows QTtA in Book 1, which is set in 1991.
» When Hagrid brought Harry to Diagon Alley for the first time, Harry heard a woman say "Seventeen sickles an ounce for Dragon Liver. They're mad." But Hagrid told Harry that there were seventeen sickles in a galleon. So that would be like saying "100 pennies" instead of a dollar.
» When Hagrid comes and gets Harry out of the little hut on the rock, they use the boat that the Dursleys used to get to the rock. So how do the Dursleys get off the rock?
» Harry buys the book "One Thousand Magical Herbs and Fungi", but later in the book it says Harry looked up 'dittany' in "One Hundred Magical Herbs and Fungi."
» Petunia Dursley says that Lily would "...come home every vacation with her pockets full of frog spawn, turning teacups into rats..." but according to ministry rules, this is illegal. If she did this in her Muggle home she would most likely be expelled as Harry almost was.
» In chapter 7, page 122, American Edition, it says that Harry looked up at the Sorting Stool, there were only 3 people left to be sorted, Professor McGonagall calls the names of 4 more people instead. ****This is because Dean Thomas was cut from the British version, but remained in the American version.****
» In Book one (it said), Prof. McGonagall brings out a 4-legged chair with the sorting hat (to the sorting ceremony). In book four (it said) she brings out a 3-legged chair with the sorting hat. What happened to one of the legs?
» In Harry's letter from Hogwarts it says he could bring a cat, an owl, or a toad, but Ron brings his rat, Scabbers.
» It says in Book 1 that Marcus Flint is in his 6th Year (American book). He is still at Hogwarts in Book 3. This would mean he was in his 8th year and students only have seven years at Hogwarts. ****JKR said in an online interview "He had to do a year again! :-)"****
» During the chess match, it said that Ron was the knight in the giant chess set. However, it later said that he had to 'move ahead one' so the Queen could take him, opening the path for Harry to checkmate the king. If he was a knight, he could only move: ahead one, sideways two, or ahead two, sideways one, like an "L".
» It said in PS that by drinking the Elixir of Life it would make the drinker immortal, but later in the story Dumbledore says to Harry that the Flamel's had enough Elixir stored in them to set their affairs straight. But, if drinking the Elixir of Life makes you immortal, then if you drank some you would NEVER die. Immortality means you can never die.
» In PS when Harry is under the Invisibility Cloak and running away from Snape, he says that he thought he was near the kitchens. However, in GoF, Fred and George have to tell Harry where the kitchens are.
» In PS, it mentions that the snake in the zoo winked at Harry. No wonder Harry was so surprised -- snakes don't have movable eyelids.
» In the chapter "The Sorting Hat", Nearly Headless Nick says that he hasn't eaten in "nearly four hundred years", but in CoS, Harry goes to his 500th Deathday Party, meaning that Nearly Headless Nick has been dead for 500 years, not 400!
» In PS, Ron visits Harry in the hospital wing, and says, "You missed the last Quidditch match, we were steamrollered by Ravenclaw without you..." But when Harry's rejecting Ron and Hermione's advice to not ply in the match that Snape will be refereeing, Harry says, "There isn't a reserve seeker. If I back out, Gryffindor can't play at all."
» If Petunia Dursley had already gone through the experience of having a family member leave for Hogwarts, why did she stare when Harry named Platform 9 3/4 as the departure point of the Hogwarts Express? They didn't keep Lily's talent secret: "...my mother and father ... were proud of having a witch in the family!"

PHILOSOPHER'S STONE movie
» When Dumbledore looks at the mirror of Erised, the door should be on his right but there is just a wall.
» After the kids have seen Fluffy and return to their dorms, Hermoine goes left, when earlier her dorm was on the right.
» As the children sneak past the guard dog fluffy, he dribbles on Ron's jumper. But the jumper is dry when they fall into the Devils snare.
» At the start of the term feast, Harry is sitting on the right of the table with Ron. When the food appears, he is on the other side next to Hermoine.
» In the chess game, Hermoine takes her position as the queenside castle on a black square. Queenside castle is on a white square.
» When Harry is looking at his mother in the mirror, you can see a reflection of a slide projector or camera.
» When Harry, Ron and Hermione return from the forbidden forest and they are sitting round the common room talking about what they saw, Hermione says Voldemort's name.
» When Hermione is looking at in the binoculars at the Quidditch match, it looks like the girl behind her is giving her bunny ears! ****Watch it in slow-mo. I think she's gesturing to something with two fingers.****
» In the Hogwarts Express when Ron and Harry are introducing each other, the camera is on Ron then switches to Harry, then back to Ron. In the first shot of Ron his part in his hair is in the middle, but in the second it is on the side.
» When Hermione is first shown on the Hogwarts Express, she is wearing blue stockings under her knee high socks, but then when they get off the train she isn't.
» In the very beginning when Harry is getting his first letter he picks up the mail and there is 3 letters. He looks at them in this order: postcard from Marge, then a bill, then the letter to Harry. When he puts one behind the other he covers up the seal, but when the camera goes to show that his name is on the mysterious letter and he looks at the back, the other letters aren't covering up the seal of Hogwarts.
» Whenever Harry comes up with the idea that Hagrid was probably tricked into telling Quirrel about how to get past Fluffy, Harry is talking and the whole time Hermione is mouthing Harry's lines.
» Hermione is wearing a different skirt at the sorting than on the Hogwarts Express.
» When Harry comes down after catching the Remembrall, there is a delay before the class starts running to him.
» When Harry and Ron arrive late for class the cat turns into the professor but when she walks towards them she doesn't have her glasses on but when she talks to them she does.
In the scene of their first flying lesson, the teacher tells them to kick off from the ground after she blows her whistle. The next shot is of everyone's feet and she blows her whistle and no feet kick leave the ground, except Neville, who simply lifts off.
» When Ron is eating and Nearly Headless Nick pops out of the chicken, if you watch it frame by frame, you can see that Ron reacts about four frames too early.
» At the first flying lesson when Malfoy is about to fly, we see Hermione looking up in the sky before Malfoy gets that high.
» During the Quidditch match, when Hermione and Ron are talking, they mouth each other's lines.
» The Hogwarts Express is definitely not big enough to hold all the students who are going to Hogwarts. If you figure that there are around 10 students in every year and there are 7 years and 4 houses, that is roughly around 300 students and the train is not that big.
» When the trio is under the cloak, Hermione tells Ron that he stood on her foot, but Ron is behind Hermione so he shouldn't have been able to step on her foot.
» In the scene where Harry is entering the Restricted Section of the library, he pushes open one side of the door, but when it has just started swinging, the other side starts moving as well, even though the actor hasn't touched it.

CHAMBER OF SECRETS book
» In the first editions, at the end of CoS Dumbledore tells Harry that Lord Voldemort is the last remaining ancestor of Salazar Slytherin. But it should say that Lord Voldemort is the last remaining descendant of Salazar Slytherin.
» George says that his mum has always wanted a house-elf to do the ironing. But if house-elves get freed by their master giving them clothes then wouldn't they be automatically be free? ****Mrs. Weasley wouldn't want the house-elf to leave, and the house-elf wouldn't want to be freed, so it wouldn't leave even though it had clothes.****
» Dobby seems to be Apparating and Disapparating inside the grounds of Hogwarts. He also seemed to Apparate and Disapparate while Harry was in the hospital wing recovering from his arm accident. But Hermione says many times that it is impossible to Apparate and Disapparate inside the grounds of Hogwarts. How can this be?****Maybe House elves have their own magical powers and can disappear at will in a different way to Apparating?****
» In their Hogwarts Equipment list, it says the Lockhart book "Wanderings with a Werewolf." However, later in the book, it mentions "Weekend with a Werewolf."
» In Lockhart's equipment list, it says "Year with the Yeti" but he then mentions his book "Year with a Yeti."
» After Fred, George, Ron and Harry arrive at The Burrow after flying the car, Mrs. Weasley shouts at Fred first; "You will not," snapped Mrs Weasley. Then she says "And you two," glaring at Ron and Fred. It should say George as she has already spoken to Fred.
» On page 182 of Book 2, Harry is still in the hospital. But it says: "Harry woke up on Sunday morning to find the dormitory blazing with winter sunlight and his arm reboned but very stiff." He wasn't in the dormitory. He was in the hospital.
» It says in CoS that Nearly Headless Nick "took several deep breaths, and then said, in a far calmer tone, 'So what's bothering you?'" However, in GoF, Myrtle says that ghosts do not breathe: "When I can't ...when I haven't...not for ages..."
» Hermione tells Ron and Harry that one of the ingredients for the Polyjuice Potion is lacewings, and that they have to be stewed for twenty one days. But then it says Ron pours dead lacewings on top of the leeches. They couldn't add the lacewings already, it being only their first day making the potion. » It says that Colin Creevy held an ordinary Muggle camera. However, in the magic world, muggle technology doesn't work. » The books state ghosts cannot eat or drink, yet Nearly Headless Nick is revived with the Mandrake Potion. How could he be revived if you had to drink the potion? » The people who were petrified in book 2 because of the basilisk were not killed, because they were looking through some type of lens, mirror or glass. So why would Moaning Myrtle have died? She was wearing glasses at the time of her death, with glass thicker than the matter that makes up a ghost, so logically she would have been petrified, not killed. ****If Myrtle was crying when she died, she would most likely have her glasses off. And when she heard a noise she probably wiped the tears off her eyes and then she saw the basilisk. Besides, if simple glasses are adequate protection, then Harry would be in no danger since he wears glasses, and JKR wouldn't have made it that easy.**** » On the day of Harry's Birthday, Rowling says, "and then, exactly a year ago, Hogwarts had written to Harry..." but they had actually written before Harry's 11th birthday. He'd been receiving them before, he just never had the chance to read one. So technically he had been written to before his 11th birthday.
CHAMBER OF SECRETS movie
» In the flying car, when they are try to get into the 'flying gear' (when getting away from spiders), Ron pulls down; but when Harry helps, they push the gear up.
» In the dueling scene, when Snape pulls Malfoy back onto his feet, a cameraman is visible on the far left of the screen.
» In the Quidditch scene, Harry breaks his right arm and cradles it on his chest, but when he is laying on the ground after he falls off his broom, he then leans directly on it when he sits up to get away from the bludger. In the shot immediately afterward, he has his hand cradled in front of him again.
» When Harry arrives at the Weasley's we see the clock that shows where everyone is. We see the twins' and Ron's picture moving to show they're home, but no-one else's picture is in the same place. Shortly afterwards we see that everyone else is already home, except Mr. Weasley.
» After the car spits them out and the car drives away and they are chasing after it, if you watch closely you can see the shadow of someone driving the car.
» In Moaning Myrtle's bathroom, the mirrors don't reflect at all, they're very dirty. But when Harry changes into Goyle, his face is clearly reflected in one of the mirrors.
» When Harry is fighting the Basilisk on top of the skull in the Chamber of Secrets, you can see that there is a safety tip on the end of the sword.

PRISONER OF AZKABAN book
» In June 2004, JKR informed the various publishers and translators of her books of two corrections which she wanted made to all future editions of book three. They are:
> Chapter 3: "So all that remains, " said Fudge, now buttering himself a second crumpet, "is to decide where you're going to spend the last two weeks of your vacation..."
which would become
"So all that remains, " said Fudge, now buttering himself a second crumpet, "is to decide where you're going to spend the last three weeks of your vacation..."
> Chapter 4: "I don't want to make him miserable, I want to put him on his guard," roared Mr. Weasley. "You know what Harry and Ron are like, wandering off by themselves -- they've ended up in the Forbidden Forest twice!"
which now becomes
"I don't want to make him miserable, I want to put him on his guard," roared Mr. Weasley. "You know what Harry and Ron are like, wandering off by themselves -- they've even ended up in the Forbidden Forest!"

PRISONER OF AZKABAN movie
» During the dinner scene at the Dursleys, Dudley is shown in a close-up watching a game show where a young woman is putting on large headphones. But when the shot returns to the whole room, you can see the girl on the TV putting on the headphones all over again.
» When Harry goes back to Hogwarts and they stand before the Fat Lady portrait she refuses to let them in because she's trying to show them she can break a glass with her voice. When she cannot she smashes it upon a brick wall behind her right shoulder. Later in the movie after the students gather around the Fat Lady's painting after it's slashed, the wall isn't there.
» As the Knight Bus begins to appear, Harry falls back onto the ground, leans on his arms and in the front shot his sweatshirt is off his right shoulder, but in the next side shot, as he still leans on his arms, both sides of his jacket are properly on.
» In the scene when Hermione removes the invisibility cloak from Harry who is sitting on the rock crying, a few flakes of snow fall on his shoulder. The next shot of Harry immediately after shows no snow on his shoulder.
» On the Knight Bus, as Stan Shunpike holds the newspaper in his hands the position of the hat on his head changes in subsequent shots.
» In the scenes when Harry is in the double decker bus, the attendant on the bus has acne on his neck that keeps changing. Sometimes there is a big "whitehead", and other times it's just a red mark.
» In the scene where Hagrid is telling Harry, Ron and Hermione that Buckbeak must be executed, you see Harry in the background sitting on a rock and he stands up when he hears the news. In the very next shot from behind, Harry is suddenly sitting down. There are no ripples visible from the big rock Hagrid's just thrown into the lake either, only ripples radiating from his body, rather than from the splash impact.
» The song "Something Wicked This Way Comes" is staged with a mixed choir, with a majority of girls. However, to the trained ear, you can tell the song is sung by an all-boys chorus. » Revealing: The first time the bus conductor shows Harry the newspaper with the picture of Sirius Black on the front, one of his fingers disappears underneath the moving picture for a split-second.

GOBLET OF FIRE
» In Chapter 8, Ludo Bagman welcomes everyone to the "four hundred and twenty second Quidditch World Cup." Quidditch through the Ages tells up that that the Cup was first held in 1473, and held every 4 years since. That means that the Cup had been held around 130 times by 1994. Nowhere near 422.
Also, if the Cup is held every four years from 1473, then 1993 and 1997 would be Cup-years, not 1994.
» The now famous wand order issue was corrected in later editions of the book. In the original version, when Prori Incantatem (reverse spell effect) happened in the graveyard, James Potter's echo appeared before Lily's. But, since the spells were happening in reverse, and we know from PoA that James died first, Lily should have appeared before him. The passage was changed in later editions to have Lily come out first, which is now the "official" version of events.
» This isn't a mistake in the book, but I'll put it in anyway because it's to funny. If you don't get it, just read it again. It may take you a few reads to work it out. "On July 8, UK publication day of Goblet of Fire, an astonishing 372,775 hardback copies were sold. In the US -- where Rowling is believed to be the first author ever to occupy the top three slots on The New York Times best-seller list at the same time -- a nation of bleary-eyed children stayed up for the midnight launch to snaffle 3.8 million volumes." (Reader's Digest December 2000 "J.K. Rowling: The Wizard Behind Harry Potter" by Tim Bouquet).

ORDER OF THE PHOENIX
» Dennis Creevy goes into the Hogs Head for the DA meeting in Hogsmeade -- but Dennis is only in second year.
» When Ron's shiny new Prefect's badge arrives, it is described as being scarlet and gold. It was a "large P... superimposed on the Gryffindor lion." According to Chapter 9, Harry "had seen a badge just like this on Percy's chest on his very first day at Hogwarts." But the badge Percy wore wasn't scarlet and gold. It was silver. The description from PS reads: "He (Percy) had already changed into his billowing black Hogwarts robes, and Harry noticed a shiny silver badge on his chest with the letter P in it."
» Everard, the former Headmaster who left his portrait in Dumbledore's office to tell someone that Arthur had been attacked, said that he traveled to the portrait of "Elfrida Cragg" so he could get a better look. The name on the Famous Wizards card and in Quidditch Through The Ages is Elfrida Clagg. She was a Chieftainess of the Wizard's Council in the 1300s. She banned using a real live bird in Quidditch, leading to the invention of the Golden Snitch.