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.]
It's Only Rock and Roll - S3-E11
Visible crew/equipment: After Ralph walks into his house with Bill and Dak, when Bill explains to Pam that Dak will be spending the night, the T-mark is visible on the floor in front of Bill. (00:31:05)
Tiptoe Through the Penfolds - S5-E3
Continuity mistake: Although Danger Mouse is supposed to be on his own, when he turns a corner in the car, in the overhead shot, you can see Penfold sat next to him.