The Long Legs of the Law - S2-E1
Revealing mistake: At the very beginning of the episode, Leonard Pearce is waiting for the cue for his character to start looking for his teeth. He's standing in the living room, between his room and Del and Rodney's room. (00:00:25)
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 Greatest American Hero (1) - S1-E1
Continuity mistake: While Bill and Ralph are in the car, John Mackie appears under the ship carrying the case with the suit. After John places the case in the car's trunk he walks back towards the ship empty handed, but in the last shot of John standing under the ship he's still holding the case.
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.