The Dark Archon, is a very expensive unit, and shouldn't be created unless you need it. It's a spell caster, meaning that it shouldn't wander around by itself. It's also not a very fast unit, so try using upgraded shuttles to get the job done.
The Dark Archon has few powerful spells, but like most spell casters, it takes time to charge up. The feedback spell is a really good counter to queens, since the zerg need queens to take out your templars. Since your dark archon can pop each one for only 50 mana, I think it's a fair trade. Feedback is also a good spell to take out medics. With a full 200 energy, 4 less medics will definately change the battle.
Maelstrom is a mass lockdown spell for only organic units. It's quite expensive, however infantry and all zerg units will be immobilized, and won't be able to attack as well. I doubt the spell will be useful on terran since marines usually hide in bunkers, and rarely make attacks out in the open. 
The Zerg however are hurt greatly, since all there units are targets, making the spell very usefull. The spell has almost the same power as psionic storm, since any unit that is frozen, is a sitting duck. Also the spell is instantaneous, meaning that once casted, it will affect those units right away, unlike psionic storm, where the units can still run. It also helps to prevent casualties since immobilized units can't attack.
Templars are sometimes hard to use in battle, since they're vulnerable to broodling. However the dark archon can't be broodling, so there is no way a Zerg player can stop one instantly.
Mind Control is an interesting spell of the 3. It has its strengths and weaknesses. I really don't like this spell since it takes 150 to cast, which takes a long time to charge up. Also it will deplete your dark archon of shields making it vulnerable. Unfortunately the dark archon can't fly, which makes it even harder to use mind control. Mind control acts like broodling and yamato gun, meaning it takes one unit away from your enemy. Mind control doesn't have the versatility of the yamato gun, which can take out defensive structures. I can't find a purpose for using mind control, unless you want free upgrades, or another race to control.
