In early scenes the filmmakers went to some effort to make Cyclops appear taller than Wolverine, but about half way through the film they just stopped, and suddenly Wolverine appears considerably taller than Cyclops (consistent with the difference in height of the actors themselves).
(at around 1h 14 mins) Between when Cyclops blows open a door in the Statue of Liberty, and when he sees Jean in peril, he gains and loses a pair of gloves between shots.
(at around 46 mins) Xavier says he is unable to find Magneto's signal from Cerebro. We later see that this is because Magneto wears a stealth helmet. But Magneto's omnipresent accomplices Sabretooth, Mystique, and Toad, do not have such helmets, and no similar cloaking devices are ever mentioned. Therefore, Xavier could still see their locations and reasonably assume that Magneto is in the same general vicinity as them. It is odd that this simple logic wouldn't occur to Xavier, who is supposed to be a genius.
Outside the train station, exhaust from one of the police cars can be seen moving back into the tailpipe, indicating the shot is running backwards.
(at around 40 mins) When Wolverine stabs Rogue, his claws go through the front and out the back. She heals herself using Wolverine's powers, but there is no blood on the front of her night gown and the fabric is still whole (where the claws went through). This is due to the fact that the "rating goal" for the film was set to PG-13, which means they can't show blood flow - and showing a shredded gown without blood would be odd.
(at around 2 mins) The Nazi Schutz-Staffel guards are wearing steel helmets. These were only used in combat situations, which did not include taking in and sorting victims for genocide. Camp guards wore "garrison caps" instead.
(at around 38 mins) The camera is visible in Cyclops' glasses when he is in Logan's room and says, "Oh, and Logan: stay away from my girl."
(at around 44 mins) When Mystique as Bobby Drake (Shawn Ashmore) approaches Rogue to warn her away from the school, Rogue clearly mouths the word "Shawn" but her voice says "Bobby".
(at around 39 mins) When Wolverine accidentally stabs Rogue, his claws come out from the tops of his hands, the way they do in the comic series. In all other scenes, however, the claws appear from between the fingers.
(at around 4 mins) Marie, in her first scene, points to a map and says "Niagara Falls" which is on the New York-Ontario border, but her finger is touching the Minnesota-Wisconsin border.
Before and during the fight at the train station, the time of day changes from dark to light several times.
(at around 1h 16 mins) When Toad is struck by lightning, the lightning hits the pole first, and then electrocutes Toad. While the pole is grounded, there is enough power in a lightning strike that the field would still affect Toad (though not as visibly as shown). In addition, Storm does, after all, have some control over lightning.
(at around 11 mins) When we see Wolverine's first full cage fight, every hit he took or made should have sounded metallic due to his adamantium enhancements, but we only hear the sound when Wolverine himself hits his opponent.
(at around 23 mins) When Wolverine is at the mansion after the initial car accident. We see him removing the sticky electrode pads from his chest which leave circular red marks on his skin. These marks remain on his skin for the rest of the shot, though they should have healed seconds or less like his other injuries in film.
(at around 2 mins) The Nazi policy sorting of newly-arrived victims of genocide into two groups - one to be murdered on site and one to be enslaved - was called "selektion" and usually involved SS doctors such as Doctor Josef Mengele, who made the selection according to a particular captive's state of health as he perceived it. In the movie no such officials are present. When this scene was re-shot 11 years later for X-Men: First Class they got this right.
The sharpness of Logan's claws changes to suit the situation in different scenes. The claws easily slice though the metal wire fence when fighting Mystique but he is able to pull her towards him with the metal chain stuck on his claws without slicing through the chain. (Also, when on the Statue of Liberty his claws slice easily though the spikes on the statue's head but when he is climbing up the side with his claws they only puncture the statue they don't slice though it once they're in, even though all his body weight must be hanging on his claws alone.)
(at around 1h 14 mins) In the Statue of Liberty, after Toad spits his slime on Jean Grey and he falls, you can see the rope that was holding him up and where it connects on his back.
(at around 1h 23 mins) During the fight atop the Statue of Liberty, Sabretooth throws Wolverine away from the statue's crown. In the next shot, their positions are reversed, with Wolverine's back to the crown.
(at around 54 mins) When Magneto has Wolverine floating in the air at the train station, and the camera zooms into Magneto bending his claws, you can see two Phillips head screws on the palm side of each claw down by his hand.
(at around 2 mins) The Nazis separated the men from the women the minute they stepped off the train once they arrived at a concentration camp. Erik and his father would have been separated from his mother long before they made it as far as they did in the film.
(at around 18 mins) When Wolverine hits the fallen tree, he and Rogue lunge forward before hitting the tree. Hitting the tree, Wolverine goes flying through the windshield and you can see the whole windshield is flying out but looking back at Rogue, it is back but cracked. In a real collision, he would have just hit the steering wheel and windshield and not fly through the windshield that far. He would need to be sitting on top of the car in order to fly out of the car that far when hitting the tree. Lastly, when Wolverine is told to wear a seat belt, they are not moving very fast but when they hit the tree, Wolverine flies out the window a distance one would need to be going over 100 to do so. If he was moving fast enough the whole front end of the truck would be crushed.
(at around 2 mins) The star on Erik Lehnsherr's father's coat at the beginning changes sides from the left to the right.
(at around 1h 29 mins) When Jean Gray is checking Logan after the fight you can see a pink bra under her jacket. The camera then switches to Logan and when it returns to Jean Gray the bra is missing and her coat closed up.
(at around 1 min) In the Nazi scene, the Schutz-Staffel guard in the watch tower is manning a MG-42 multipurpose machine gun, an equipment usually issued to front line troops only. For behind-the-line duty such as guarding concentration camps, obsolete weapons or those captured from occupied countries such as France or Czechoslovakia were usually issued.
(at around 1h 30 mins) When Xavier and Magneto are in the plastic prison, the chess pieces on the board change between shots after the guard comes in.
(at around 38 mins) When Rogue walks into Logan's room just before he stabs her, his sheets are pulled up to his armpits, but as she approaches the bed and the camera angle changes the sheets are about his waist.
(at around 1h 14 mins) During the Statue of Liberty fight, Mystique kicks Wolverine in the side of his head. Seeing as Wolverine's skeleton is laced with adamantium, it should have broken her foot. Yet, she shows no signs of injury or pain from it.
(at around 1h 23 mins) When Wolverine swings around the spike on the crown of the statue with his claws, he lands with his right hand held forward, claws unsheathed. In the next shot, his left hand is held forward just before he leaps.
(at around 51 mins) When Wolverine is talking to Rogue on the train, she begins to cry and he pulls her head to his chest. In one scene you can see his lips moving (speaking the next line) without sound, until the shot changes and he speaks the line in sync.
(at around 1h 23 mins) When Wolverine is thrown off the head of Statue of Liberty, he stops himself by hanging on his claws; at that moment, they pierce through the head near Jean Gray and Cyclops who are trapped inside near the top. In one of the next shots we can see Wolverine hanging on his claws much lower in the head - somewhere around the ears and the chin of the Statue.
(at around 1h 30 mins) When Magneto tells Prof. Xavier that the plastic prison won't hold him and the war is coming, the shot from behind Magneto's head shows his mouth still moving, even though he has stopped speaking.
(at around 21 mins) When Magneto takes Wolverine's dog tag from around Sabretooth's neck, the clear string attached to pull it can faintly be seen.
Minor inconsistencies in each mutant's power (especially relating to matters never clearly defined in the comic books) are not goofs. Since it is all make believe, they can do whatever the writers say they can do, even when contradictions seem to occur.
(at around 30 mins) Senator Kelly boards a helicopter that is dark green and white in color with the Presidential Seal and the "United States of America" printed on the side. After they take off, the helicopter is blue and white and does not have the Seal nor the U.S. logo on it.
The straps inside the Statue of Liberty that hold the skin of copper to the iron frame were originally iron, then were replaced with stainless steel during the refurbishment. At no time were they green as shown.
(at around 44 mins) When Rogue and Bobby are sitting on the bench talking, Rogue's hair keeps switching from being behind her shoulder and then in front of her shoulder.
(at around 1h 35 mins) Stuntwoman Kathryn Anderson's name is misspelled in the end credits as "Kathyrn".
(at around 52 mins) In the train station, as Sabretooth is coming up behind Storm at the ticket window, he throws the guy behind her out of the way. The line attached to the stuntman is visible in this shot as he is yanked out of the way.
(at around 1h 15 mins) The chain-link fence door is very "floppy" when Mystique hits Wolverine with it in their final fight.
(at around 20 mins) When Storm and Cyclops stop Sabretooth at the beginning of the film, Cyclops places his hand on the visor to use his beam. In the next shot the beam is seen but both his hands are down, away from the visor.
In the flashback scene that shows Magneto using his energy transfer machine, when Mystique is helping him up by the hand, you can see that some of her blue makeup came off on his hand.
Senator Kelly's aide is named Henry Peter Gyrich in the script and Guyrich in the end credits.
(at around 1h 30 mins) When Magneto concedes that he has been checkmated and knocks the king over, a pawn that was in the previous view of the chessboard is missing but the knight still holds it to checkmate.
(at around 57 mins) Outside the train station, Magneto makes a police officer's pistol fire at his face and stops the bullet with his Powers. Once he stops it, the bullet should lose his velocity and should not entitled to go further (Similar to catching a ball in mid-flight. Once it is caught, it won't continue its movement if it is released again).
(at around 15 mins) After the bar fight, Logan drives off; as he stops, the tires leave snow tracks. As he starts up again, and before the snow could have buried them, they disappear.
(at around 31 mins) Mystique pushes Senator Kelly back after he yells, and when he lands against the seat we see her right foot wrap around the back of his head. In the next shot, her foot is just starting to move around to his head.
(at around 57 mins) In the sequence where Rogue is abducted and Magneto blackmails his way out, he telekinetically fires a police officer's pistol at his own face from a short distance, stopping the spinning bullet in mid-air without harming the man. He would not have been able to stop the non-metallic combustion gases though. From that short a distance, even blanks can severely hurt or kill people.
(at around 21 mins) Orientation of Magneto's helmet on the desk during the first scenes in the Brotherhood's lair.
(at around 30 mins) In the helicopter scene just before Mystique is revealed, Senator Kelly finishes a phone call and gives the phone to his assistant, Henry Gyrich, who is really Mystique in disguise. The false Gyrich appears to place the cell phone in the inside pocket of his jacket. Seconds later, Gyrich transforms into Mystique's true, naked form with no jacket and no place to store a cell phone. The film doesn't show the cell phone falling out, or Mystique removing the phone. It simply disappears.
The stealth helmet that Magneto wears is supposed to protect him from Charles reading his mind or locating him with Cerebro. The helmet covers the thickest part of his skull, leaving the thinnest part fully exposed--his face. It is unreasonable to assume that this would not be a big enough area for the professor's powers to penetrate.
(at around 31 mins) The amount of sun hitting Senator Kelly in the helicopter scene with him and Mystique.
(at around 14 mins) In one shot, Logan is smoking a cigar and his truck window is up. In the next shot, outside the truck, his window is down. Inside the truck in the next shot, his window is once again up.
(at around 1h 6 mins) When Mystique is driving the boat to the Statue of Liberty, the captain's head is below the window in long shots, but in a different place in close-ups.
(at around 51 mins) When Logan puts his arm around Rogue while they are on the train, he puts his hand on her shoulder. In the next shot his hand is on her head.
(at around 1h 24 mins) When Wolverine says to Sabretooth "I'm not finished with you yet", he points with his middle claw, but in the next shot, he's pointing with all three.