Plot hole: In the episode 'Backwards' most of the things that happen on 'Backwards Earth' are correct, except, of course, in reverse. But there is an exception: in the scene in the Cafe, when the waitress comes to 'dirty' the table, she tips a box of trash on the table. If you play this scene backwards, the trash leaps from the table into the box. Even on a 'backwards earth' I can't believe that trash spontaneously leaps about... (00:09:30)
Continuity mistake: The time that the events involving the crew of Red Dwarf keeps changing throughout the series. At various times, references are made to the date, which is stated as being in the 21st, 22nd or 23rd centuries. Examples: In 'Stasis Leak', the date reference is stated as being 2077 (21st century). But in 'Ouroboros', the date is stated as being 26th November 2155 (22nd century). Also in 'DNA', Lister says he is an enlightened 23rd century guy.
Deliberate mistake: In the first few series, it is suggested Lister and Kochanski barely know each other. In 'Balance of Power' Holly says that Lister has only ever spoken 173 words to her. However, by series 4 Kochanski is referred to as Lister's ex-girlfriend with whom he shared a relationship. In the series 4 documentary, Doug Naylor explains that Lister's attitude towards Kochanski was immature in the first series which is why they changed his back story from wanting to be with Kochanski to actually having been with her by series 4.