They said nothing is affecting the mouse input, which is not true. You have the answer on the last page of Crytek Q&A thread. They'll have to look into it more.
It might be linked to frame rate: I'd guess the tutorial ran at 100+ fps whilst the campaign is 40-50. input lag is idd correspondent to FPS... but the problem was that having aprox 60-80 (beyond 60 fps) input lag was still there. Even if you have 50-60 fps you shouldn't notice much of input lag but in beta it was like having rocks attached to my gun so as i move to the left it takes some time to get there, it's not "instant" like it was in C2.