Continuity mistake: When Spartan and Phoenix are fighting in the sewers, Edgar Friendly shoots his gun at Phoenix and you see the catwalk that Phoenix was on tip to its side and Phoenix dropping down to the ground with the plank of the catwalk right below him. When Phoenix lands on the ground the plank is nowhere to be seen. It should have been right below him. (01:19:25 - 01:30:30)
Continuity mistake: When Spartan and Huxley arrive at the cryogenics place to battle Phoenix and what remains of his gang, Phoenix sees them on the monitor walking into the building and you see Spartan on the left and Huxley on the right. The camera angle changes to an inside view and Spartan is now on the right. (01:38:35)
Continuity mistake: When Spartan switches seats with Huxley in the police car, the outside shot shows him get into the back seat. When the shot switches to Huxley in the driver's seat, we can see the back and Spartan isn't seen anywhere in the car. (00:42:40)
Continuity mistake: When John Spartan is frozen in the cryochamber, at the beginning of the movie, if you watch during the credits - while the time is going by the small circular monitor that is on his chest and head, it changes from the left side to the right side of his chest and head in almost every shot. (00:10:10)
Visible crew/equipment: When Phoenix falls through the glass at the museum into the LA exhibit, you can see him sliding down a safety rope. His feet are even in the position to be sliding down the rope. (00:49:15)
Continuity mistake: The guard Phoenix throws through the glass case has on footwear which resembles socks. As he is smashing through the glass, he has on heavier leather boots. (00:44:30)
Revealing mistake: Towards the end of the movie, when Spartan goes after Phoenix in the cryolab, he fires several rounds at him with his Beretta 92 handgun and the slide locks back indicating he is out of rounds. The camera pans to a shot of a crane as he inserts a new magazine and is about to pull on the slide. However, when the camera returns to him, he pulls the slide back and a round can be seen ejecting out, indicating he hit the slide release before pulling the slide back.
Other mistake: During the scene where Phoenix is questioning the leader of the future society in his office, he says at least one word (hell) that he should have been fined for, and isn't. We see that there is a ticket printer in the room in a later scene, when Savage sets it off during his own confrontation. (01:06:50)