Continuity mistake: When Storm and Cyclops are in the train station, and Toad whips Cyclops goggles off, he punches a hole through the ceiling of the train station behind him, yet the hole changes from behind him to above Storm between shots. (00:50:30)
Continuity mistake: When Cyclops and Storm are in the train station, Storm is held up by Sabretooth, Cyclops spots this and starts to walk over to help. He stretches his arms out between a lot of people to push two people out the way, yet when the shot changes to Toad's POV all the people around him are at least two to three feet away from him. (00:50:30)
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: 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: 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)
Visible crew/equipment: After Senator Kelly's death, watch Storm as she runs away. On her right, a microphone wire is visible. (01:00:40)
Suggested correction: Doesn't appear to be a wire, but rather a line in the fabric of the shirt she is wearing. There is one on the other side that you can see when she walks in to the room. Also, I don't think they wear microphones. Usually there is a boom mic overhead. You can see examples of the boom being used in the special features disc of X-Men 1.5 that shows you behind the scenes footage.
It is a battery pack for a mic. Bryan Singer admits this in the director's commentary.
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)
Continuity mistake: In the Statue of Liberty scene just after Wolverine, Storm Cyclops and Jean go through the metal detectors, they walk off and watch in the background, you can see Wolverine walk past Cyclops yet in the following shot he is walking past again. (01:09:25)
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)
Audio problem: Just before Cyclops shoots his beam which breaks the toad-slime off of Jean Grays face, he says "Don't move," however HIS MOUTH doesn't move. (01:12:30)
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)
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)
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)
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)
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)
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)