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.
Factual error: While it is true that lithium carbonate can be used to treat depression and other psychiatric disorders, it cannot be administered in gaseous form. It is a very stable salt and only starts to form vapour at 1,310 degress Celcius. Spraying it about as a 'mood stabliser' at that temperature, as Kryten does, is going to kill everyone on the spot.
Suggested correction: A couple of explanations come to mind. After 3 million years, the lithium carbonate may have become contaminated or mutated, resulting in it becoming a less stable salt and/or a change in its chemical structure. Another explanation is that Holly just made a mistake. They have a proven track record of mistakes, saying the wrong things, and generally being stupid.
Salts don't mutate - they don't have genes. If Holly "just made a mistake" and the chemical being sprayed about by Krtyen wasn't lithium carbonate (or it was contaminated), then it would not work as a mood stabiliser. Since it does, it was lithium carbonate and the Boys From The Dwarf are going to die horribly.
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.
Factual error: Kryten tells everyone that the matter paddle transmits matter in digital form from one place to another at the speed of light - he is very clear on this point. He then locates Waxworld, which is 200,000 light years away. Okay - so when they use the matter paddle to transmit themselves to Waxworld, why doesn't it take them 200,000 years to get there?
Suggested correction: Kryten says that the paddle sends them via subspace, so they will reach it almost instantaneously (rewatch the scene, he never says they'll travel at lightspeed).
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: 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?
Suggested 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).
Trivia: On the DVD, you can watch this episode backwards. This way, not only can you find out roughly how they made this episode and find out what 'reversed' people are saying, you can hear someone shout 'ACTION' right before the brawl scene.
Suggested correction: This episode is available backwards on YouTube, too.
Revealing mistake: At the start in the cockpit of Starbug, the green screen behind Lister is visible instead of the painted starfield that should be there. (00:02:35)
Suggested correction: That is because Starbug is parked inside Red Dwarf at the time, and the stars wouldn't be visible.
Continuity mistake: Just after The Inquisitor is frozen when Lister and Kryten switch gauntlets, the glove gets onto Kryten's hand in one camera cut. (00:24:30)
Suggested correction: He's holding the gauntlet in his hand, but the angle of the camera makes it appear that he's wearing it.

Continuity mistake: In the forest, Lister and the Cat take a poster off a tree. They then show it to the man who gives them a lift. The poster is different to the one in the forest. (00:16:05)
Suggested correction: If you look at 00:13:47, you'll see that the closest tree has an odd poster. The other trees have the poster that they showed to the man that gives them a lift.
Emohawk - Polymorph II - S6-E4
Revealing mistake: Both Ace and the Emohawk get sprayed with the liquid Dyllinium, yet only the Emohawk becomes paralysed. (00:26:55)
Suggested correction: Ace is a hologram. Even though he is hard light, he cannot be harmed. Which is why he was able to jump on the grenade and not be harmed. So the gas spray wouldn't have harmed him either.

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)
Suggested 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.
Continuity mistake: When the Cat picks up the golf clubs, his hair is sitting on his left shoulder. In the next shot it is behind his back. (00:10:40)
Suggested correction: His hair moved to his left shoulder when he turned his head and picked up the clubs, but you can see his hair go back behind him when he straightens his head.
Factual error: The polymorph goes through a metal pipe and a tap which bulges and becomes mis-shapen. The tap then changes back to its original shape, which is impossible. (00:18:00)
Suggested correction: It's impossible using today's technology, but maybe not in the future. Maybe they have metallic-like materials that flex back to a previous form after deformation.
Revealing mistake: When Baxter puts the Cat's head in the drinks machine and says hot bovrill, Kryten can be seen mouthing the line behind him. (00:22:20)
Suggested correction: Kryten is not mouthing the line "Hot bovril." He is just moving his mouth slightly up and down, which coincidentally happened to occur when Baxter was saying the line.
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.
Revealing mistake: In the sleeping quarters, Rimmer turns on a swivel chair. This would be impossible as he is a hologram. 3.10. (00:03:10)
Suggested correction: As a hologram, this would also mean Rimmer could not touch or sit on the chair. The chair was likely a hologram as well, used to be operable by Rimmer. It has been shown before that Rimmer can still interact with other holographic objects.
Revealing mistake: When Lister is in jail with the Cat, as he is looking out of the window, he is naming famous people. He says "Mussolini" before he actually looks at him. (00:10:55)
Suggested correction: First, Lister is shown looking out the window throughout the scene, and second, he still has an entire view of outside the window within his eyesight. Lister likely already seen Mussolini within his eyesight before turning to face his direction, which he likely did to assure himself it was definitely Mussolini.
Visible crew/equipment: When the Cat says "You mean to help you get out if the program freezes" on Blue Midget, a soundman can be seen crouching behind the control panel. The top of his head is visible in the top right of the screen. (00:14:10)
Suggested correction: That is not the head of a soundman crouching behind the control panel, or any crew member for that matter. What you are seeing is Kryten's hand moving around.