Factual error: None of the vehicles in the logging camp, purportedly in the Canadian Rockies, have correct licence plates for either Alberta or British Columbia, the provinces the Rockies are located. They are not the white on blue that British Columbia was using in the early to mid 1980s, nor the black on yellow of Alberta during the same time period. They aren't even the red on white for Alberta or blue on white for BC that are currently used since the late 80s/early 90s.
Revealing mistake: When the old couple who give Wolverine clothes are first driving towards their house, there is an aerial shot of them driving over a bridge. This is supposed to be set in Canada (drive on the right) but it was filmed in New Zealand (drive on the left). They are driving on the right but the arrow on the road is on the left side.
Revealing mistake: When Logan is at the old couples' house and checking out his new claws in the bathroom, watch where they come out of his hand carefully - the animation of his CG claws doesn't totally replicate the movement of his hands, making it look as though they are floating around his knuckles.
Other mistake: When Logan is talking to the old man in the barn, in the "This was my son's jacket, try it on" scene, he is sitting on the motorbike, and when he gets up, the bike doesn't move up on its suspension. A few seconds later, when he sits back down on the bike, the suspension sinks a lot due to the weight of his adamantium skeleton.
Continuity mistake: After Logan is shot twice in the head with adamantium bullets by Stryker , an overhead shot of him shows the bullets at different heights on his forehead. In this shot, the bullet on his right is noticeable higher. After Logan sits up and they begin healing, the left bullet appears higher on his forehead at an almost even height to the right one.
Factual error: When Wolverine leaves one of the compounds, he slashes through the door with both hands, creating an "X" in the door. After the second slice, the portion of the "X" where the cuts actually crisscross remains in the door, when in reality the pieces would fall out as they wouldn't be attached to the door any longer and would be floating in air.
Continuity mistake: Wolverine fights the Blob in the boxing ring and knocks him out. When he interrogates the Blob on the whereabouts of 'the island' he draws his claws in a horizontal line, but when the shot switches back (beside Wolverine's shoulder), his claws are in a vertical line facing the Blob's face. The alignment of the claws switched from horizontal to vertical every time the shot changes.
Continuity mistake: When Logan and Sabretooth stand back-to-back during the fight with Deadpool, watch their positioning: Logan's left hand is directly above the edge that leads down to the inside of the reactor. But after Deadpool jumps over them and starts hitting Sabretooh, Logan is now positioned so that his right hand is directly above the edge.
Continuity mistake: When Wolverine has been catapulted from the truck, Wolverine looks to the right as if to slash the helicopter blades on the right side. Viewing from above the chopper the blades are spinning counter clockwise initially. Once Wolverine reaches the chopper blades, the blades are spinning clockwise, enabling him to slice and dice.
Deliberate mistake: After Wolverine arrives at 3 Mile Island he approaches through a thick fog. Above him are a series of conveyor belts that are used at a coal power plant, not a nuclear plant such as 3 Mile Island. The belts are unique to coal mines and coal power plants, and would not be found at a nuclear power plant. The filmmakers obviously couldn't film on the site of a nuclear plant, so filmed on a coal plant to fill in.
Continuity mistake: At the end of this movie Wolverine is shot in the head, making a hole in his adamantium skull. However in X-Men we saw an X-ray of his skull, and there was no hole in it. Logan's skull and brain would've healed from the adamantium bullet fired by Striker, but the bullet hole in the adamantium forehead plating should have been visible in the X-ray image.
Factual error: The movie takes place six years after the Vietnam War; mid to late 1970's (if the Three-Mile Island accident depicted in the film is supposed to be the actual accident, then it would be 1979; either way, it is sometime in the 1970's). The 20-dollar bills on the ground in New Orleans have Andrew Jackson's head in the large offset oval; a redesign of the currency that wasn't issued until 1998.
Continuity mistake: In the scene where Wade (as the Mutant Weapon XI) & Logan's show down begins, Logan's claws release slowly, and in retaliation, Wade gets his Right hand's sword out. This is the front view. After Striker types in the command to "engage", the front view for Wade still shows only the right sword out. However, when the camera angle shifts to the left profile of Wade attacking, both the swords are out.
Revealing mistake: When Wolverine and Gambit are fighting, at one point Wolverine starts slicing apart a fire escape stairway Gambit is on, causing it to slowly collapse downwards. But if you pay attention, the scene is completely ridiculous. The fire-escape slowly collapses, in defiance of physics, at just the right speed for Wolverine to be able to slice it apart piece by piece (when in reality it should have fallen down all at once and then just fallen over), the pieces that Wolverine slices seem to just explode into nothingness when there should be pieces of metal building up around him, and even beyond that... The effect itself also looks very unrealistic. Poorly put together effects sequence that doesn't make any sense if you pay attention.
Continuity mistake: When the boy runs out the house at the beginning he is barefoot - we see this in a close up. When he runs off with his brother into the woods they are both wearing wellington boots.