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.
Deliberate mistake: Though the film takes place over the course of several weeks, at night there is always a full moon.
Deliberate mistake: In the scene where we see Bella in her room looking out the window, the months are passing, but she is always wearing the same clothes. (00:28:30)