Factual error: At the Award Ceremony, Alex is announced as a Lt Commander, but he is wearing Lieutenant's stripes on his shoulder. (01:57:22)
Suggested correction: It was a spot promotion that he didn't know he was getting. The Admiral called him LCDR to let him know he was getting promoted.
Other mistake: Early in the movie, It is said in the movie that the force field is 300,000ft in altitude, and approximately 2 miles in diameter. It is far less than 300,000ft high, and larger than 2 miles wide.
Factual error: During the soccer match with Japan, Hopper is kicked in the face and had blood coming from his nose onto his lips and chin. Then while talking to a Japanese player the blood is gone, then a few seconds later when he makes the penalty kick the blood is back on his face.
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)