Did you know that Super Mario Brothers 2 is a total remake of a game called Doki Doki Panic? I found a webpage with all the info about the 2 games, but I forget what it is. I'll post it here when I find it again.
There are a few warps in Super Mario 2. I'll post them here in a couple days.
There are 3 places where you can skip most of the stage and battle Birdo very early:
1. Place one, stage 1-1. When you enter the cave with the waterfall, jump over the waterfall after you go up the ladder. Go all the way to the left, and there will be an enemy and a couple bombs. Chuck the enemy off the ledge, and time the bombs right so that when you throw them off the ledge to the left, you will destroy some of the blocks. Enter that door, and you will appear outside. Jump up over those ledges and on the other side, will be Birdo.
2. Place two is in stage 3-1. Start as the PRINCESS. Go up the clouds in the beginning of the level, and then climb the vine at the top. Find some mushroom blocks, and them 4 high on the very left of the cloud. Jump on top of the mushroom blocks, and FLY all the way to the left. Enter the door, follow the path, and find Birdo.
3. Place three is in stage 6-3. After you climb the ladder at the beginning of the stage, Go all the way to the left and let yourself sink most of the way into the sand. Repeatedly press the A button, and hold left. You will move UNDER the wall and appear on the other side, where a door is. Enter the door, and beat Birdo.