Factual error: Between Earth and the Moon the crew of the spacecraft have an EVA in which they walk on the ship's metal hull with magnetic boots. At one point an astronaut inadvertently slips both boots off the hull and drifts off into space, helpless. There is a long shot of him drifting away in which his body spontaneously spins around 180 degrees and then stops rotating, which is all a violation of conserved angular momentum.
Factual error: At the end of the movie, Joe Gillis is shot twice in the back and once in the chest before falling dead into a swimming pool. However, no blood from the wounds is ever seen in the pool, even after his body has been floating in it overnight.
Factual error: When the two escapees from the POW camp are in the anchor room of the ship they are on, they leave the harbour and the pilot boat leaves them, but then the chain for the anchor goes out, but they are moving away from the port, why on earth would they be dropping the anchor? If anything they would make sure that all the chain is in the anchor room and the anchor would be on deck.