Attention!!!
Okay, maybe this will help. I don't believe this problem is unique to the Airaid system. I have the Injen system and John's tune, and I'm experiencing the same thing. See here:
http://www.ft86club.com/forums/showthread.php?t=15526
In summary, if I try to open the throttle quickly from a low rpm state, like rolling from 5mph in 1st gear, the car builds revs slowly and begins to bog and jerk near 2000 rpm. It sometimes gets better, and I usually have to let go of the throttle. Progressively opening the throttle is okay.
I haven't had a chance to contact John about this since I know he is a busy man. I can't say for sure if it's related to the tune or the intake, or both because I'm not usually in a situation where I need to floor it from a really low rpm state.