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.]
The Best Desk Scenario - S1-E9
Continuity mistake: After the successful junkyard arrests, when it cuts to Ralph and Pam walking outside at the high school they stop at Ralph's new office. Its exterior door is white with three nameplates attached, and a brick wall perpendicular to it, but a few minutes later, while Bill and Ralph are arguing it cuts to another exterior shot of Ralph's office, and now the door is blue with one nameplate attached, and the brick wall has vanished. (00:45:25)
Visible crew/equipment: When Miss Hawk is speaking to Edward by the well, the boom mic can be seen in the top right of the screen.
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.