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. (01:06:54)
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.
Revealing mistake: During the montage that introduces Xavier's School about 27 minutes into the film, you briefly see Cyclops shooting several Frisbees/clay-pigeons out of the air. Watch closely, and you will see that the falling debris from all of the clay-pigeons simply "fades away" shortly after each one explodes. They aren't burning up or disintegrating from his beam. You can see them "fade away" as the animation finishes when each one explodes. A shortcut in the CGI rendering.
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. (01:18:28)