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...
Continuity mistake: When Lister (in Rimmer's body) pleads the Cat to lend him his body, he says 'how else can I pilot White Midget?'. In the next scene, the Blue Midget is being piloted, and White Midget was originally abandoned for Starbug. (this mistake was admitted by the crew)
Other mistake: At the start of the episode, there is a spoof Star Wars-type caption, which spools up the screen very quickly. Too quickly to be read, in fact... which may explain why few people have noticed that the last line of the caption, "And now the Story Continuums...", is written twice.
Plot hole: If everything goes backwards, shouldn't Kryten and Rimmer have got fired, done their job and then got hired? Rimmer & Kryten discovered that everything was backwards in the cafe earlier in the episode. At the club they did their act and then got fired. Put this 'forwards' and it becomes wrong.
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.