Continuity mistake: When Tom Cruise first encounters Gene Hackman, Gene is nonchalantly leaning in a doorway with both hands in his pockets. In the next shot, Gene is holding a briefcase that wasn't there before. It's a good thing the briefcase arrived, since Gene makes mention of it immediately after.
Continuity mistake: As Tom Cruise is leaving Mud Island on a monorail car he passes another car with a Firm henchman in it. They see each other and the man gets out and runs across the bridge to catch Tom as his car stops. This is impossible since there are really only two cars which end up on both sides at the same time.
Continuity mistake: In the scene when Abigail and Mitch part. Abigail gets into the car and starts the engine but doesn't reach for the seatbelt. The camera switches to Mitch, he says "Take care of yourself" and then it cuts back to Abigail driving away but this time wearing a seatbelt. The time between the two cuts is too short for putting the seatbelt on, especially because Abigail didn't even make a move to reach for it before the first cut.