Revealing mistake: In the train scene if you look closely at Vincent's ear as he steps off the train ready to shoot Max and Annie, it looks like he has an earpiece or some kind of small blood pack in his ear. (01:44:05)
Plot hole: Near the end Max calls Annie, using the number on the card she gave him, to warning her about Vincent's arrival. But why is there on the card the number of the law library on the 16th floor and not Annie's office number or her cell phone number?
Stupidity: Vincent's choice to cut the power to the building that Annie is in does nothing but waste enough time for Max to save Annie. It would have been easier just to go up to kill her and he probably would have gotten away from the police if he did so.
Stupidity: When Max is in the federal building and shoots Vincent, he and Annie get into the elevator and go to the first floor. Knowing that Vincent would take the stairs down to the first floor, why didn't Max and Annie stop on the 12th floor, or any floor, get out, and call the police from there. It would have taken Vincent quite a while to figure out what floor they were on, and they could've kept moving from floor to floor and Vincent would've never found them.