Continuity mistake: When Smith and Connor arrive at the Nakamoto tower and are exiting the elevator on the 46 th floor, you can see in several shots that Smith's suit is wet on the shoulders. However as he was going up the elevator the suit wasn't wet at all and even during the whole scene in the 46th floor, the suit changes from wet to dry as angles change.
Visible crew/equipment: When Sean Connery first examines the girl's body, he touches her neck while wearing latex gloves, and rubs his thumb against his fingertip. Then he sniffs his fingertips, and at that moment the large shadow of a mike boom or some other equipment moves across his forehead.
Continuity mistake: In the scene where Wesley Snipes and Sean Connery are in the car together for the first time, on the way to the murder scene, it is raining out. The camera shots pan from a wide angle of both actors to close up shots of each. During this you can see the windshield wipers are different depending on the shot. When you see the top of the blades in one shot, one blade covers over the others track. In the next view it doesn't. It's obviously a static car, but it's less obvious that it was two different cars used.