Continuity mistake: During the climactic landing sequence at the end, the point of view shifts rapidly from head-on to alongside and back. Watch carefully at the first side-on view just as they're touching down; the nose of the shuttle says "Columbia". When it switches to the next head-on view, the wings say "Daedalus".
Continuity mistake: When Frank is stopped in the lobby after leaving Gerson's office if you look out the window behind Frank you see a couple walk by, a woman in a light suit and a man next to her. The shot than shifts to Gerson and back to Frank, you again see the couple walking by, within 30 seconds.
Continuity mistake: The character Jerry, played by Donald Sutherland, snaps off one arm of his sunglasses that the doctor gave him. He uses it to assist him in fixing the door that was jammed shut. When they are suited up and coming back to Earth it shows him with the sunglasses back on from both sides of his head and the arm is on the glasses, not broken off anymore.
Continuity mistake: The US flag that was in the back-left corner of Gerson's office (between the map and the window) when Colonel Corvin first visits to offer Team Daedelus' service is gone later on, when General Vostov is in Gerson's office. (00:34:25)