Continuity mistake: When Harris is briefing the new group for the first time, Hightower loosens the leg of Harris' chair so that it breaks when Harris sits down. When Harris gets up from the middle of debris, the next shot shows an innocent looking Hightower and the chair is intact in front of him.
Continuity mistake: The picture of Cpt. Harris in the newspaper in the beginning is different than the picture that was taken. When his picture is taken, he's holding the tail so it forms a U-shape. In the newspaper, the tail is in a different position and his eyes are opened wider.