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?
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?
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... (00:09:30)
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.
Plot hole: Lister is not allowed any dangerous objects that he might try to commit suicide with, yet when he is with the canaries on their missions, he carries an assault rifle. The canaries aren't always supervised and it would be impossible for a guard to stop any of them putting a gun to their head and pulling the trigger. (00:05:05)
Plot hole: In S2 E2 Better Than Life, Rimmer mentions that his brother Frank was 6' 5" by the time he was 11 due to their father pulling him on a tractor, however in S3 E5 Timeslides, the picture of Frank Rimmer's wedding shows Frank to be of fairly average height, and not 6' 5".
Plot hole: The barroom tidy scene in the pub makes absolutely no sense. It is established that this fight started because Lister and the Cat uneat a man's pie, which causes the man to punch Lister, and then the barroom brawl happens, but the events are reversed due to this version of Earth being set in a backwards reality. However, if the events of this fight are put into chronological order, this would mean that Lister uneating the man's pie and being punched by him would have been the last thing to happen during this fight, as it was the first thing to happen in reverse order, and therefore, would also means that there would have been no real reason for the pub patrons would get into a brawl in the first place, as nothing had occurred at that time. (00:23:15)