Factual error: Kryten tells everyone that the matter paddle transmits matter in digital form from one place to another at the speed of light - he is very clear on this point. He then locates Waxworld, which is 200,000 light years away. Okay - so when they use the matter paddle to transmit themselves to Waxworld, why doesn't it take them 200,000 years to get there?
Continuity mistake: When Kryten decides to be a mechanoid again, Lister gets up and grabs his jacket and swings it around his shoulders. The camera cuts to Kryten for a second then back to Lister, who now has his jacket on fully. The amount of time the camera was away from Lister would make this impossible for him to put the jacket on that quickly.
Continuity mistake: In the scene where Lister is talking to human Kryten, just before Lister sees the photos, keep an eye on Lister's hat. It is perched on top of his head with about an inch of hair showing, yet the next shot shows the hat covering all of the hair, then it goes back to an inch of hair showing again. There is no time for Lister to have adjusted his hat between cuts. It is clear the line had to be re-shot.
Continuity mistake: When the Cat and Lister are trying to cook an egg with a bicycle powered hair drier, you can see the Cat holding a frying pan. When Lister gives up and gets off the bike, Cat picks up a spatula with his other hand and starts poking the egg with it. However, in the next shot, he is shown with both hands on his hips. It's an instant cut with the same conversation continuing, so he didn't have time to put them down.