Factual error: Kryten tells everyone that the matter paddle transmits matter in digital form from one place to another at the speed of light - he is very clear on this point. He then locates Waxworld, which is 200,000 light years away. Okay - so when they use the matter paddle to transmit themselves to Waxworld, why doesn't it take them 200,000 years to get there?
Continuity mistake: In George's memorial service, the extras are totally different in the shots from George's point of view to the shots from the back of the room. Look for the woman with brunette hair and orange overalls - she's there in the forward shots but missing in the reverses. The chairs, tables, props, costumes and character placements are all completely discontinuous.
Continuity mistake: When Lister and Rimmer see Cat just after Holly explains how he evolved, Rimmer runs at Cat screaming before he passes through him and we hear a crash off screen to indicate Rimmer has just run in to something. He is a hologram and is not solid, so no sound should be heard. [The original version did not have this mistake. The sound effect was added for the now defunct Remastered series.]
Continuity mistake: At the start of the 'Welcome Back George McIntyre' reception scene, Lister, Chen and Selby are throwing things at Rimmer, then Rimmer looks around. In the next shot, Lister and Chen are looking round to their left, Selby is stabbing between his fingers, Rimmer is now looking straight forwards and Petersen has appeared from nowhere.
Visible crew/equipment: When the Red Dwarf crew are talking about who Legion is (after Lister has poured his bucksfizz), Kryten then says, "Could our very presence here have inadvertently awoken him?" As he says this, at the left side of the screen the end of a camera lens pulls away.
Factual error: While it is true that lithium carbonate can be used to treat depression and other psychiatric disorders, it cannot be administered in gaseous form. It is a very stable salt and only starts to form vapour at 1,310 degress Celcius. Spraying it about as a 'mood stabliser' at that temperature, as Kryten does, is going to kill everyone on the spot.
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...