Other mistake: Each time Cage is on the dropship along with all the other soldiers, the dropship is attacked and all the other soldiers release themselves from the plane onto the beach. When Cage lands on the beach, note the area he is standing in. Every time he drops onto the beach, he releases himself earlier or later than the previous time, but despite this, he always seems to land on the beach in the precise same spot each time. The dropship was also attacked and began spinning out of control and was not in a fixed position, so there is no chance he would have landed in the same spot even if the dropship was over the same location.
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Factual error: In the opening sequence just before Minute 1, after the asteroid is reported to have hit Hamburg (Germany), it is shown in red how the mimics spread through Europe. But wrongly this spreading is originating from the center of Europe (somewhere in Austria) rather than in Hamburg (on the far north of Germany). You can even see in the next shot how it spreads from Austria to Germany, Czech Republic, Slovakia and Hungary, which makes no sense if the origin is supposed to be the far north of Germany.
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.