Deliberate mistake: Almost trivia, but not quite. When Mystique's looking through the guard files to find a suitable candidate, lots of photos flash up very quickly before she finds the guy she uses. Of note is that Bryan Singer pops up in guard uniform (with his own name), and so does someone called "Donner, L". This is most likely referring to Lauren Shuler Donner, one of the producers, and sex is specified as "F", but the photo is of a stubble-coated man. (00:23:10)
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.