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.
Factual error: The helicopter markings and paint schemes are exclusive ONLY to POTUS (President of the United States). Senator Kelly, even thought he's trying to get a Presidential bid, wouldn't be allowed to fly around in aircraft marked like that.
Revealing mistake: The "copper" straps used to restrain the heroes in the Statue of Liberty are actually made of foam or some other malleable material. They flex considerably as the characters struggle.
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).