Continuity mistake: In the forest, Lister and the Cat take a poster off a tree. They then show it to the man who gives them a lift. The poster is different to the one in the forest. (00:16:05)
Suggested correction: If you look at 00:13:47, you'll see that the closest tree has an odd poster. The other trees have the poster that they showed to the man that gives them a lift.
Continuity mistake: Rimmer wears a hat with an antenna on the right hand side when on Starbug, and after arriving on Earth, but when he and Kryten are walking through the streets later on, the antenna is now on the left side of his hat, and is far more extended. (00:02:20 - 00:08:00)
Continuity mistake: When Kryten is piloting Starbug and gently "eases forwards", there is a shot shown from behind Starbug where it is driving out of the cargo bay to the exit, and it is shown a couple feet off the ground. When Starbug exits Red Dwarf in the next shot, Starbug is suddenly much higher above the ground. (00:04:20)
