A couple questions spring to mind:
Why do the focused classes get +3 in the primary stat vs the hybrid classes? Presumably a balance issue?
Yep. The focused classes get +3 in the primary stat to offset their lack of selection when it comes to Class moves. Hybrid classes get two lists to mix/match from, I figured I'd give, effectively, a free stat advance to the guys with the more limited selection.
Is No Shit Pilot a tech or personal move?
It's a Personal Move. The design philosophy was that your Race/Class combo really only matters for combat, while your "role" in the party, i.e. medic, pilot, "face" man, etc. would come from your personal moves. It's not perfect, as there are some combat-y personal moves, but I tried to keep the Personal moves more "thematic" and the Class moves more "battle-oriented"
Some 'balance' thoughts- so take these for what they are worth:
Some racial +1 bonuses will come up much more often, and more importantly can be triggered by player description (e.g Asari) vs say the Quarians, who really don't want to have to use their bonus. :)
Adrenal Rush is way more powerful and flexible than Singularity (not a surprise, as it comes from the slightly powergamey Touchstone) - killing someone disables them for more than one tick. And yet, the consequences of failure are worse for Singularity. Maybe consider swapping them? The Soldier also gets better gear.
Yeah, I find that I'm not over-concerned with "balance" when it comes to Apocalypse World, mostly because the game is very narrative-driven, and all characters start as kinda badasses no matter what. To address your specific nitpicks:
yes, the Quarians will rarely use their Basic Move bonus compared to, say, Krogan or Salarian, but when they DO use it, they'll REALLY need it :)
Adrenaline Rush is, yes, very badass (as is the Touchstone move from which it came). In my mind this is ok since the Soldier is otherwise pretty limited when it comes to "cool" thematic combat moves. Most of what they get are ammo powers. Singularity, however, is a cinematically cool move that has multiple applications, like battle-field crowd control etc. I also changed Singularity in the more recent revision to make it a bit cooler than it was.
I've been running two different groups of five players each, each game running once every other week, for a couple of months now and I've been really impressed with the character concepts / builds people have come up with. The human Adept who focused in Cool and Will and uses the Singularity / Dominate combo really rules the battlefield, as does the (obviously min-maxed) Krogan soldier with Carnage :) But even so, everyone gets a role to play, everyone can feel like they're doing something awesome, and most importantly, it seems to really convey the "feel" of the Mass Effect games.