Continuity mistake: In the Statue of Liberty, when Toad has shot his slime at Jean Grey's face, we see Cyclops shoot his optic beam to free himself from the room he was trapped in. Then he rushes to Jean's aid. If you look closely you can see that the gloves he was wearing, as part of his costume, are no longer there when he takes the slime off of Jean's face. (01:15:37)
Continuity mistake: In the medical bay at the end, Jean's medical coat keeps jumping from positions on her shirt between shots.
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.