Continuity mistake: When Hopper climbs to the roof of the convenience store, the time displayed in the upper left corner of the screen (presumably a video surveillance camera) goes from 12:11.57 to 12:12.12, then back to 12:11.34.
Continuity mistake: The Sampson is hit by one shell at first, leaving a large hole on the port side of the bow. But when it's being pelted with shells during the second volley, the hole in the bow is gone.
Continuity mistake: When the Phalanx on the Sampson starts shooting at the incoming projectiles, it's a short-barreled version. When the shot cuts, the barrels are much longer.
Continuity mistake: The USS Sampson has no Close In-Weapons System at the bow when the movie starts, but uses one to counter enemy fire later.
Continuity mistake: After the Sampson is hit, and the captain says "continue fire", there is a shot straight from the front of the ship. That shot is flipped, you can see the damage done by the shell is now on the other side of the ship.
Continuity mistake: At the scene when Hopper is playing soccer he receives a kick to his face, however the blood on his face changes between shots.
Continuity mistake: In the scene on the mountain where the Hawaii police ask Mick and Sam to leave the mountain. Mick and Sam ask why and they are told during the conversation that the aliens have blocked all cell phones, radio and internet but in the next scene with the police they use a radio to communicate with each other.
Suggested correction: Even if jammed, a radio signal could still potentially reach a few dozen yards to another vehicle, even if it couldn't go a mile or more. Power drops proportionally to the square of distance, so the power at 50 feet away is ten thousand times higher than at 5000 feet away (roughly a mile), and a million times higher than at 10 miles.
Continuity mistake: The missiles fired at the aliens during the boardgame inspired scene, are shown to be a Standard Missile (SM-2) when leaving the launcher, then a Tomahawk cruise missile when flying towards the aliens.
Continuity mistake: Towards the end of the movie, when the USS Missouri gets hit by the mother alien ship, the scenes show all of its turrets, or at the very least 6 out of the total 9 turrets getting blown up in to pieces and some of them being snapped, but a few scenes later she is firing back at the alien ship through all 9 of her turrets.
Continuity mistake: When the old guys are getting the battleship ready, there are two on the walk way turning the crank to withdraw the path. When the angle changes to show the walkway moving, the two guys vanish.
Continuity mistake: When Sam and Mick are on the mountain, they meet Dr. Zapata who emerges from behind a bush with a twig in his hair above his forehead. In the next cut the twig has moved to the top of his head, and in the next it is gone.
Continuity mistake: When the USS Sampson gets blown up by the aliens, the front of the ship explodes first, then the rear, but in the next sequence the rear explodes first, then the front.
Continuity mistake: Hopper has just stepped on to the alien craft and is looking up at the vertical wall that is the ship's hull. The amount of sunlight on his upturned face significantly changes in consecutive shots. In the first close-up shot, only the left side of the face is in sunlight. In the immediate next shot, as the camera zooms out vertically, his entire face is bathed in much stronger sunlight. (00:40:25)