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?
Red Dwarf (1988)
1 plot hole in Can of Worms - chronological order
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.
White Hole - S4-E4
Rimmer: The thing about Captain Oates... The thing you have to remember about Captain Oates... Captain Oates... Captain Oates was a prat.
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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.