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.
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.
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?