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...
Other mistake: At the start of "Backwards", 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.
Revealing mistake: Near the end of the episode, Kryten and his employer are seen arguing in supposedly backwards English. However, when you watch the episode how the people of earth would see it on the second DVD, Kryten and his employer aren't speaking English, they are just speaking plain gobbeldy-gook, even although when you see the people of Earth talking on the DVD they speak correctly.
Revealing mistake: When Rimmer stands up from underneath the table, just before he says, "Thanks for your support" to Lister, listen very carefully and you can hear the stunt director saying "Action!" backwards. This shot was the splice point between the reversed and the regular footage. (I know this mistake is listed as being in the 'backwards version' on the DVD, but it is in the regular broadcast version too - you just have to listen harder for it.)