Revealing mistake: At the point where someone gets a small bruise on the upper arm, the crew are all in a pile and thrashing about on the floor. There are 5 pairs of legs instead of 4. Arthur is in his pajamas, Zaphod is in orange trousers, Trillion is lying on top of Ford and Ford is too far away for them to be his legs. [The fifth pair of legs belong to the person playing zaphod's third arm - doesn't mean it's not a mistake, but that's where they come from.]
Revealing mistake: When Ralph picks up the guy who was stealing mustangs and takes off with him over his shoulder, while they're in the air the cushion under Ralph is visible in the closeups. (00:18:00)
Continuity mistake: When Edward and Tracy open the lid of the chest in the tower, Benger puts his hand on Tracy's shoulder and Edward has both his hands on the lid. In the next shot, he now has one hand on it.
Continuity mistake: When Colt Seavers is chasing the villains in the golf cart, the camera equipment on the back of the cart keeps disappearing and re-appearing.