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. (01:12:15)
Continuity mistake: In the Statue of Liberty, Cyclops reaches up to his visor with his left hand and blasts away the door that was trapping him. Yet from behind he lifting up his right hand. (01:14:25)
Continuity mistake: The chain Mystique wraps around Wolverine's wrists during their fight scene near the end of the movie mysteriously disappears shortly after that moment. (01:15:07)
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: Right after Wolverine slices the tip off one of the Statue of Liberty's prongs, he strikes a dramatic pose: left arm cocked at his chest, right arm extended. In the next shot, his right arm is at his shoulder and his left is in front. (01:23:00)
Continuity mistake: When the police rush into the Statue of Liberty, a cop stands over a Statue Museum guard. In one shot the guard is on the floor with his left arm outstretched, but in the following overhead shot the arm is underneath him. (01:25:05)
Continuity mistake: When Wolverine leaves the mansion at the end of the film, he has a curl in his hair whilst talking with Rogue. Once he exits the mansion, the curl has disappeared. (01:32:55)
Continuity mistake: During the final scene with Xavier and Magneto playing chess, there is a pawn missing from the board after Xavier leaves and Magneto pushes over his King. (01:33:47)
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: When Wolverine and Rogue are in Wolverines truck, just prior to the crash, we see them driving near huge trees with thick leaves that can't be seen through. When Rogue says the line "You really should wear your seatbelt", the view out her window shows a handful of trees that one can see through for a mile.
Continuity mistake: When Senator Kelly meets Magneto for the first time, it's outside and cold. When you see Kelly his breath shows blowing to the left of the screen. But when you get the reverse angle of Magneto and Mystique their breath also goes off to the left of the screen. It should be blowing to the right.
Continuity mistake: When Logan is driving his truck the road is free of snow, but when he gets out because he hears Rogue in the back, the road is covered with snow.
Continuity mistake: In the medical bay at the end, Jean's medical coat keeps jumping from positions on her shirt between shots.
Continuity mistake: Logan stabs Rogue through her chest, but there are no marks in the front of her dress.
Continuity mistake: After the last fight Logan is lying at the top of the statue with some wounds on his forehead. In the next shot those wounds increase size and have more blood on them.
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