Continuity mistake: In the bridge fight scene where Colossus and Negasonic Teenage Warhead appear, Deadpool tries to escape Colossus' handcuffs by severing his hand. The hand that he cuts off is his left, but when he jumps off the bridge the severed arm is on his right side.
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)
Continuity mistake: When young Magneto is struggling with the guards at the concentration camp, the father's star switches from one side of his chest to the other. (00:01:46)
Factual error: Take a look at Google Earth - the section of the Golden Gate Bridge Magneto breaks off (about a mile - tower to tower plus a section each end) isn't anywhere near long enough to reach Alcatraz from anywhere on the mainland.
Continuity mistake: Gambit pushes Logan, who smashes through a wall. This hole becomes much, much smaller when Gambit climbs out into the alley. (01:10:00)
Continuity mistake: When the young mutants are showing each other what they can do, they all have a glass of cola, all four sitting on a corner of the table. But when Banshee wants to show what he can do, the glasses are instantly lined up. (00:51:00)
Other mistake: Wolverine shields Yashida from the blast, burning off all his hair. Somehow his pants manage to remain unaffected by this, as seen later when they are climbing from the pit.
Factual error: The Mountain Dew logo seen in the stadium didn't come out until 1980, despite the film being set in 1973. The changes made in 1980 were subtle, but still distinct, especially the loss of the "wave" in the "D" and the smaller hole on the "a."
Continuity mistake: Logan tries to give the Professor an injection, who pushes him away and falls over. As he falls back his left sleeve is still rolled up - the shot cuts and it's instantly right down to his wrist.
Continuity mistake: In the final fight, Deadpool says to Cable "did you feel that too?" and there's no-one behind them at all. Cable moves forwards to kill a guy on the ground, and a fraction of a second later, as Deadpool says "only best buddies execute paedophiles together" an orderly has appeared in the background, who gets shot.