Revealing mistake: After Toad spits his slime at Jean Grey he falls to the floor. You can see the tether that was holding him in mid air. (01:13:55)
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: Just before Sabretooth grabs Storm at the train station he swats a guy aside who was standing in line behind Storm. You can clearly see a wire attached to the guy to yank him off-frame. (00:52:19)
Revealing mistake: The metal bar wrapped around Storm's neck in the Statue of Liberty is noticeably wrinkled. Obviously a painted strip of foam rubber. (01:15:25)
Revealing mistake: In the middle of the film when Magneto goes to get Rogue from inside the train, he opens the train up, and if you look behind him you can see the roof of the studio. (00:51:50)
Revealing mistake: In one scene Magneto makes two police cars fly up into the air. Then in the shot when they come back down a thick wire is visible, attached to the bottom of the car pulling it down. (00:53:10)
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: When Storm is using her powers to blow Toad out of the Statue of Liberty there are things swirling around and blowing, but a rack of T-shirts doesn't move.
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)
Revealing mistake: When Magneto is lifting up Wolverine on the train, you can see screws on the bottom of his claws. His claws are natural, with metal directly bonded to them, and did not need to otherwise be attached.
Chosen answer: You are working under the assumption that Mystique would not believe this either. However, with Magneto in prison and no sign of the senator she could happily take on his identity. Also, even if Kelly was alive, after she gave a press statement backing mutants, it would be unlikely that a politician would change his mind so suddenly again and he would therefore not come clean that it was not him.
Scrappy