Revealing mistake: In several episodes, but mostly in series 6, we see lots of profile camera shots of just Lister and The Cat at the front of the cockpit in Starbug. Quite a few times you will see Lister mouth The Cat's lines so he knows when to start speaking and what to say.
Other mistake: At the start of Rimmer's exam, the invigilator orders the students to "turn over their papers and start". Rimmer reads one side of the paper, then turns it over to read another question. The back of the paper should have been blank as otherwise there would be no point asking the students to keep the papers face down before reading the questions. (00:15:30)
Revealing mistake: After the Cat's dance, Lister says 'we are outta here' and pulls the level, at which point the crew all fall back as if Blue Midget had rushed forwards. However, in the model shot of the ship it shows it scraping its foot on the floor before it runs forwards, meaning the crew should not have fallen back in their seats. (00:10:50)