Revealing mistake: In the scene where Storm and Nightcrawler rush to rescue the children from the holding cell, you see a shot of the cell where the children stand up and say "Listen..." before Nightcrawler teleports inside. If you look carefully, you will see Nightcrawler's silhouette in the shadow against the wall.
Revealing mistake: In the beginning of the movie when Wolverine puts the cigar out in his hand, you can see the mark of a wedding ring on his ring finger (Hugh Jackman is married). Even if Wolverine got married during the "blurred" bit of his memory so doesn't remember it (tenuous at best), his healing ability would have removed any ring mark. Either way it just doesn't belong.
Revealing mistake: In the part where Mystique (as Grace) and the guard are in the bathroom, right after the guard drinks the rest of the beer and passes out, Mystique turns him over and you can see the guard move his right leg to steady himself even though he is supposed to be knocked out.
Revealing mistake: When Storm is admiring Nightcrawler's body art, there's a point at which you can see the color of the actor's skin in the crease of his neck, because he either sweated off his blue makeup in that spot, or the artists didn't apply enough. There's a point toward the end of the movie where you can see Rebecca Stamos' skin in the crease of her neck as well.