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 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 the first scenes where the Jews arrive at the concentration camp, the SS guards are wearing steel helmets. However, it was standard practice in the German army (or the SS) to wear helmet only in combat situations. Taking in and sorting the Jews is not a combat situation. The SS guards at the concentration camps usually wore so-called "garrison caps," not steel helmets.
The sorting of newly-arrived Jews into two groups of those to be exterminated and to be put to forced labor was called "selektion" and usually involved SS doctors such as Dr. Josef Mengele, who made the selection according to a particular Jews's state of health as he perceived it. In the movie it seems there are no such doctors doing the selection.
In the beginning scene at the concentration camp, the SS 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 the occupied countries such as France or Czechoslovakia were usually issued.
Marie is showing her boyfriend on a map where they're going to go on an adventure. She points to what she calls Niagara Falls but where she points is far too west. Where she points is closer to Minnesota or Wisconsin than New York.
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.
During the long shot of Mystique driving the boat to the Statue of Liberty, you can see the head of someone below the window. That is reportedly the boat captain, who was in a different place in close-ups.
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.
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).
During Logan's nightmare scene in Xavier's mansion, when Rogue walks into the room, his sheets are pulled up to his armpits, but as she approaches the bed and the camera angle changes the sheets move to about his waist, too quickly and too neatly to have been thrown there during camera movement.
When Cyclops blows open the door in the Statue of Liberty, you can see that he is not wearing gloves. In the next shot, with his hand still on his visor, he is wearing gloves. In the next shot when he sees Jean in peril, his gloves are off again.
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.)
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 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.
When Wolverine accidentally stabs Rogue upon waking up from a nightmare, 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.
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 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.
Inconsistencies in each mutant's power (especially relating to matters never clearly defined in the comic books) are not goofs. They can do whatever the writers say they can do, even when contradictions seem to occur.
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 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.
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.