My wizard is wondering about taking the Prodigy move with Magic Missile. We both agree this seems a little overpowered. It would appear that it would be an auto-hit range weapon. I guess he needs to roll, and bad things could happen if he fails, but it still seems like he could cast a lot of these very cheaply.
Yes, you can. All Prodigy does is lower the level of the spell you apply it to.
Choose a spell. You prepare that spell as if it were one level lower.
Dungeon World p. 148
Assuming you apply it to Magic Missile, a level 1 spell, this means you lower it to level 0, making it a cantrip. This doesn't affect how easy it is to cast. All it means is that you don't count it towards the 'character level + 1' levels of spell you are allowed to have prepared each time you make the Prepare Spells move.
You still have to roll to cast it every time, and things can still go horribly wrong - the level makes absolutely no difference here.
Yeah you totally can! Remember though that he still has to roll whenever he casts and that the spell's level has no effect on that roll. The levels just dictate which spells he can have prepared at any one time. In effect the only impact of this would be that he can take Magic Missile as a given during preparation and prepare one more first level spell.
It sounds like you are conflating D&D and Dungeon World here.
Dungeon World doesn't use Vancian Casting. If you cast a Level 1 Magic Missile, you don't automatically forget the spell. You don't have to "memorize" Magic Missile 4 times to cast it 4 times a day, even if it's a level 1 spell.
The only difference between a Level 1 spell and a "Level 0" cantrip is that you always get all of your Level 0 spells when you Prepare Spells, while you have to choose which Level 1 spells you will have access to on a given day.
Applying the Prodigy move to Magic Missile has exactly the same not all that amazing effect on Magic Missile that it does if you apply Prodigy to Cloudkill, Fireball, Dispel Magic, or Invisibility: You save one level worth of spells when you prepare that spell. It has no effect on how often you can cast it, what the consequences are, or whether or not you forget the spell after casting.