Visible crew/equipment: At the start of the film, just after the war exercise, when the Sergeant begins yelling at the recruits you can see the outline of his microphone under his T-Shirt. (It's not his dog tags because you can see the shape and dog tags are not shaped like that.)
Other mistake: When the bunch of soldiers find Dr. Paul Foster, one of them removes the doctor's wallet from the crack in his skull. In this scene, Foster's eyes are open and seem to be red. Before and after this scene, when you can see the eyes, they are clear white. The wallet has traces of blood and brain matter on it, but the blood looks too reddish. If it is some hours old, it should look darker. (00:34:10)
Continuity mistake: When Stump is killed, we can see him falling off the cliff with the headband on his head. However, later on the movie, Amber finds his headband in the mine.
Suggested correction: The mutants could have taken his body through the mine.