Continuity mistake: When Magneto lands the Golden Gate Bridge on the island, as it hits land it is still very light. When the Brotherhood start to walk toward the island, it cuts to a wide shot of them still walking on the bridge, and it's suddenly dark.
Factual error: Take a look at Google Earth - the section of the Golden Gate Bridge Magneto breaks off (tower to tower, with a bit of overhang, 0.9 miles at most, more like 0.85) is not long enough to reach Alcatraz - the two closest points are 0.96 miles apart, and that's the very end of a pier, which most likely couldn't support the weight of the bridge anyway.
Continuity mistake: When Logan pulls out the two horns from his stomach, the camera shows two holes on the singlet as part as his wounds. In the following scenes, the holes of the t-shirt have recovered (I know Logan has healing ability, but not his clothes).
Revealing mistake: In the scene in the laboratory under the mansion, when Wolverine confronts Jean about Cyclops, there is a close up shot of Wolverine's hand holding Cyclops' glasses. In this shot there is a small cut visible on Wolverine's hand - his healing power should not allow this.
Continuity mistake: In the scene where Angel is about to be given the cure, there is a change in the hypodermic syringe used to administer the drug. As the camera shot switches between views of Angel being strapped in and Dr. Rao preparing the injection, the first view shows the hypodermic needle cover already having been removed. The camera switches to Angel then back. Dr. Rao, having completed the preparation for the injection, proceeds to remove the cover which had already been removed in the first shot.
Other mistake: At the beginning of the credits, (of the version shown in cinemas) they have mis- spelled 'Starring', they put 'Strarring'
Other mistake: When Warren/Angel refuses the cure and spreads his wings, he is looking to the left of the screen at his father. In the reflection of Dr. Kavita Rao's glasses the shot of him is not reversed; he is still looking to the left of the screen when he should in fact be looking to the right.
Visible crew/equipment: When Wolverine grabs Cyclops's sunglasses at Alkali Lake, a crew member, walking by, is reflected in the lens.