Continuity mistake: As Tom Cruise walks down a street he is being followed by a bald man. He sees the man and runs across the street and hails a cab from a street that is supposedly at a right angle to the street he was just on. However this street is actually the same street he just ran away from. You can tell because there is a small bodega in the background with a green awning. In the first scene it's lit. In the second the lights are out. But it's clearly visible, as are the other shop fronts.
Continuity mistake: Just after being followed on the curiously empty streets of Manhattan, Tom Cruise makes his way to a coffee shop. The last shot from the street before he turns to enter the shop shows not a person on the sidewalk, but the next shot of him from inside the cafe opening the door, shows about three people passing in the background.
Continuity mistake: In the scene in which Alice tells Bill about her fantasies regarding the military man, the right shoulder strap on the camisole she's wearing is up, then down, then up, then down - obviously the scene was culled from multiple takes. In addition, the stack of CDs on the window sill just over her right shoulder seems to be balanced precariously (particularly the top one) in some shots, and stacked normally in others.
Continuity mistake: In the scene where Tom has become quite paranoid and is being followed by the bald man. Well when he turns that one corner you'll notice a sign in the background on the buildings on the other side of the street which has some name an the number (212)555-5115 or something like that. Then the shot cuts to the bald guy, but when the shot comes back to Tom if you look in the same spot the sign is gone, and you can notice the outline of where the sign was.
Continuity mistake: In the scene in the orgy house, when women start walking to other people one by one: the woman which will approach Tom Cruise at one point has no neighbours in the circle (because two women at her sides already left), but later she is kneeling next to another woman with big mask, who was three 'seats' to her left earlier.