White Hole - S4-E4
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. (00:15:25)
Revealing mistake: The pyrotechnic charges are visible under the 'High' Cat and Kryten's robes, before they are shot. There is also a wire trailing behind Kryten and running up his left leg, presumably a means of detonating the charges. (00:12:45)
Gunmen of the Apocalypse - S6-E3
Visible crew/equipment: When the simulant has beamed on board Starbug, Lister and The Cat get up slowly from the table. Look closely, and you can see the shadow of a boom mic cast on Lister and The Cat. (00:07:50)
Plot hole: As the luck virus gets you what you want, it should not have cured Lister of the sexual magnetism virus when Kochanski was all over him. (00:16:25)
Suggested correction: According to the Red Dwarf Fandom page, "The Sexual Magnetism virus makes the infected irresistible. The only known anti-virus is the Luck Virus, which was discovered by accident by Dave Lister." Granted, it doesn't seem to make sense, but apparently that's just the way it works.
Continuity mistake: After Rimmer and Lister argue about the pod, Rimmer walks off and Lister steps into the observation room. As Lister steps in, his locks are over his left shoulder, then in the next shot they are over his right shoulder. (00:14:05)
Continuity mistake: When Lister picks up the camera at the start of the episode, he stands up and turns around. In the next shot, from the view point of the camera in his hand, the shot is still rotating as if he had just picked the camera up. (00:00:15)
Continuity mistake: When Lister and Rimmer are talking in their bunks, Lister says 'I've always been crazy about her'. He is looking to his right with his arm in the air, yet in the next shot he is looking down at the floor. (00:12:50)
Visible crew/equipment: When the alligator lands on the German guards, a fluffy grey boom mic can be seen at the top of the screen. (00:04:25)
Rimmerworld - S6-E5
Revealing mistake: When the Cat says 'Form an orderly queue behind the gunsight' you can see Lister mouth the line. (00:15:40)
Other mistake: When Legion stabs his left hand, everyone grabs and shakes their left hands - except Lister, who grabs and shakes his RIGHT hand. (00:22:40)
Visible crew/equipment: If you look closely when the camera follows Lister (in the scene just before the meteor crashes onto Starbug) you can actually see the edge of the set and some studio lights. (00:04:10)
Revealing mistake: When Lister slams his nose into the door of the cabinet, you can see it is nowhere near it. (00:17:50)
Continuity mistake: When the Cat says, "So what do we do with them?" Kryten disappears from Lister's left between camera shots. (00:17:30)
