Continuity mistake: When Cage lands on the beach for the first time, Kimmel gets crushed by a downed transport. The force of the crash knocks Cage to the ground. When Cage starts standing up, a transport can be seen in the upper right corner of the screen. When you first see the transport, it is closing its bay doors and banking left (left on screen, but moving right to the viewer). A closeup of Cage standing up then blocks the view of the transport. When the camera pans back from Cage, you can see the transport again. Except it's doing the exact same thing as before in the previous shot of it, closing the bay doors and beginning to bank to the left.
Continuity mistake: In the scene where character William Cage arrives by helicopter, as he exits, a soldier approaches to take out bags/suitcases. In the following shot (from a distance) Cage walks away from the helicopter, but he's still very near the helicopter. The soldier unpacking the helicopter is walking towards the helicopter however, again picking up the bags.