Continuity mistake: During the scene when Arnold carries the casket, a shot shows many bullet holes on its front side. Two shots later, these holes have disappeared. (00:54:45)
Deliberate mistake: Almost trivia, but not quite. When Mystique's looking through the guard files to find a suitable candidate, lots of photos flash up very quickly before she finds the guy she uses. Of note is that Bryan Singer pops up in guard uniform (with his own name), and so does someone called "Donner, L". This is most likely referring to Lauren Shuler Donner, one of the producers, and sex is specified as "F", but the photo is of a stubble-coated man. (00:23:10)
Revealing mistake: In the subway scene, when Neo gets slammed towards the wall (and crashes into it) it's visibly Keanu's stunt double.
Deliberate mistake: When Morpheus is facing the twins' car, the road's not all that wide, and there are concrete barriers both sides of him. After he rolls to the side and slices their car, we see a side shot, quite far back from the road, and the barrier closest to the camera has disappeared (presumably so we get a better view). In a closer view, both barriers are back again. (01:29:25)
Continuity mistake: In the scene where the police car is chasing Ben Affleck and Uma Thurman on a bike down in a tunnel, in one shot, the police car's flashing light on top is ripped off by the low ceiling. In the very next shot, the lights are still on the top. The next shot shows the lights are gone. (01:13:50)
Continuity mistake: The hole in the car windshield changes size from when the Hulk throws the dog through it to when it's shown the next morning.