New this monthPlot 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?
New this monthSuggested 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.
New this monthAlso, Holly mentioned she (it's one of the episodes that the original Holly redesigned himself to look like Hilly) didn't tell them because 'they never asked', which shows glitches, as something as important as that would normally be pointed out without asking, as it's very important to mention it.
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?
Suggested correction: Cat was a descendant of the cat Lister brought aboard Red Dwarf. Would it be possible that the new owners might have stricter security controls, and Lister was sent to Stasis for a different reason?
Inventing Deux ex machina explanations for a plot hole doesn't make it any less of a plot hole. M-Corp erases all of the Jupiter Mining Corporation's equipment, personnel and infrastructure from Lister's life. In no way is Cat a part of that. He has no connection at all to the Jupiter Mining Corporation, and until he meets him in Episode 1 no connection to Lister, either.
If M-Corp only erased JMC equipment from Lister's life, then Kryten, who belongs to DivaDroid and not the JMC, wouldn't have disappeared either. He disappears as he doesn't belong to M-Corp, not because he belongs to the JMC. Cat has no connection to M-Corp, as he wasn't a part of the JMC (as you pointed out), and is therefore erased for 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?
Suggested correction: The point of a Mexican standoff is no one is in a position to shoot first for fear of being shot themselves. We're told the shapeshifters have no problem killing each other, so as soon as the real person starts to shoot, everyone may start firing, which could result in a real person being killed. Additionally, the only time all 9 are pointing guns at each other is in the lift. Before that, it's 3 groups of Listers, Krytens, and Rimmers, so no one is facing off with their shapeshifters. The only safe way to shoot the 6 shapeshifters would be to do it at the same time, and there's no way Lister, Kryten, and Rimmer could coordinate that. And, like all Mexican standoffs, it can only be resolved from outside help.
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)
New this monthSuggested 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: 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: In the last series, a point was made that the time drive is not a teleporter, so can only send them backward and forward in time in the one location (Deep Space). So in this episode, how can they now travel to Earth with the same device?
New this monthSuggested correction: With the merging of the two universes, the time drive ended up with the faster-than-light drive from the other universe (which is also how Starbug ended up bigger).
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: The man the crew find stampeded to death had been lying in the road for a year, yet he had not began to decompose. (00:17:50)
Plot hole: Allman does not remember his trial when The Inquisitor erases him, yet Lister and Kryten do remember their trial when they are sentenced. (00:01:20 - 00:13:30)

Plot hole: At the start of the episode, on a shelf in the sleeping quarters is one of Rimmer's Army De Nord figures, which were all burned in Marooned in series 3. (00:00:40)
New this monthSuggested correction: Obviously, he has more of the figures than those that were in the chest; it's never stated that he doesn't, and he missed at least that one when packing.
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)
New this monthSuggested correction: He's in a panic. People, even mechanoids apparently, forget things in a panic.
Plot hole: The alligator that falls out of the plane with Ace hits the ground several minutes after Ace does. (00:04:25)
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: 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)