Plot hole: Cat wasn't manufactured by the Jupiter Mining Corporation and had no connection with them, being born three million years or so after they lost control of Red Dwarf. The takeover by M-Corp would mean nothing to him. Why, then, does he become invisible to Lister?
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.
Other mistake: When Cat picks up the can of Leopard lager which is invisible to Lister, he shakes it, pops the cap and sprays Lister with foam. The foam is visible but the can remains invisible, and that makes no sense. If we are seeing the scene from Cat's point of view the can and foam should both be visible, and if it is from Lister's then neither should be.
Factual error: The writer's understanding of the history of Nazism and its leaders is a bit shonky. Claus von Stauffenberg did not plant a bomb in Hitler's briefcase - he put it in his own briefcase which he planted in a meeting room next to Hitler (some berk moved it). This was in July 1944, while the last Nuremberg rally - which Lister visits, bringing back the briefcase - was in 1938. Stauffenberg didn't even join the anti-Hitler conspiracy until 1943. Red Dwarf is not an 'alternate history' - they correctly identify elements of the Stauffenberg plot and the Nazi regime, they just get them wrong.
Plot hole: At The End, Kryten, Rimmer and Lister are in a lift facing off six gelf shapeshifters - two copies of each real person, in a Mexican standoff. Nobody knows who to shoot, as they might shoot the real person instead of the shapeshifter. But the real people know they're real - all Lister has to do is shoot the two fake Listers, Rimmer shoots the fake Rimmers and Kryten shoots the two fake Krytens, problem solved. Not to mention Lister is now a soulless, unfeeling killing machine. Earlier he shot and killed a shapeshifter who could well have been Cat - he didn't know it was a shapeshifter and by his own admission he didn't care. We have already seen how fast on the draw he is - why didn't he just open fire on the six shapeshifters, Kryten and Rimmer in order to ensure his own survival?
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. (00:12:15)
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. (00:20:30)
Audio problem: 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.] (00:27:10)
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. (00:09:40)