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: 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)
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: Right after the shrinking boxers scene, Kryten says the small boxers are missing from the bunk, but you can see them right in front of him. (00:10:00)
Suggested correction: I've just watched this scene. You're mistaken. The boxers aren't visible when Kryten turns back to the bunk. The trunks were bright red. The only red thing visible in the scene where Kryten is looking at the bed is the "no smoking" sign, which is on the side of the bed, right in front of him.
Plot hole: When Holly discusses what the crew can do as a result of activating the self-destruct, she comes up with three options which all end with "And get blown up." Since it turns out that Holly disconnected the bomb "ages ago," wouldn't she have known that they wouldn't be blown up?
Suggested correction: It's been a while since I've seen the show, but Holly is more than a little eccentric and silly, and if memory serves, it's implied he/she has gone a bit "senile"/glitchy due to sitting around mostly unused for three million years while Lister was in stasis. From the sound of it, it's likely just that Holly was being a bit thick and forgot in the moment about disarming the bomb.
The Last Day - S3-E6
Plot hole: In this episode Kryten has no idea how to operate a bazookoid, yet earlier on in 'Polymorph' he was able to change the settings of one from standard to heat-seek and fire it without a problem. (00:24:45)
Suggested correction: He's in a panic. People, even mechanoids apparently, forget things in a panic.