Continuity mistake: Kryten needs to ask what a pub is, yet in the episode "Backwards" he and Rimmer worked in one for three weeks as the comedy act "The Sensational Reverse Brothers", and, later, were involved in a brawl in the same pub. Originally, the episodes were to be shown in a different order, which explains why the mistake occurs, but doesn't excuse it.
Plot hole: In season 2 episode 2 Better Than Life, Rimmer says his brother Frank was 6 foot 5 by the time he was 11. However, in season 3 episode 5 Timeslides, the picture of Frank Rimmer's wedding shows he is around Rimmer's height which would be about just under 6 foot.
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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.