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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.)
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.
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.
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.
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.
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.
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.
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.
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.