Continuity mistake: When Wolverine crashes into the tree knocked over by Sabertooth, notice that the entire front of the truck gets completely folded up and the windshield breaks into a thousand pieces. In the next frame, Wolverine gets thrown through the unbroken windshield and the front of the truck is practically undamaged...
Revealing mistake: Right after the scene where Sabretooth dispatches the Liberty Island guard, the camera switches to a head on shot of Magneto's boat ferrying the torch. As the camera moves upward, you can distinctly see the head of someone crouching down next to Mystique as she captains the boat and it is actually the guard that was the boat pilot.
Continuity mistake: When Mystique reveals herself to Senator Kelly on the helicopter, her blue body is appearing and it shows Senator Kelly watching for a few seconds, but when it shows Mystique again, the blue body thing continues from the part it left off at. It should have been to her legs at the rate it was going at before.
Continuity mistake: At the start when Rogue walks into the bar, when she walks towards the cage, note all the things around her from the camera's perspective (which is from behind her): the wooden plank in front of her which she walks around, and the burning can to the left of the screen. When the camera cuts to the front, the wooden plank is not there and neither is the burning can (now to the right of the screen).
Revealing mistake: In Toad's final scene of the movie, when he is beginning to fight Storm, he leaps into the air onto the balcony railing. If you look at the back of his belt, his wire is very, very obviously visible. There are several times within the movie when Toad or Storm has a wire showing, but none so obvious as that one.
Continuity mistake: When Mystique and Wolverine are fighting, Mystique lifts up a chain link door and Wolverine cuts through it with his claws. It splits and the two pieces go separate ways, yet in the following shot the door is on the floor near Wolverine with only one side cut.
Continuity mistake: Just after Sabertooth has dropped the Senator into the water, the mutated Senator pops out of the water. In the first shot, he is facing the boy, but in the next shot he has his back to the boy, then facing the boy again. Also, when he pops out the water he is only a few feet away from the boy's yellow boat, yet in another shot he is much farther from the boat.