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.
Episode #4.3 - S4-E3
Deliberate mistake: Before the gas explodes in the sewer, you can see the base of the Davy lamp glow red. Except that in real life this doesn't happen; the flame simply turns blue and grows taller in the presence of gas. This was probably done to make the scene more dramatic, though.