How I'm Spending My Summer Vacation - S2-E17
Plot hole: When Kevin is upset about Paul leaving for summer and is just lounging around the house, he asks why they can't go on vacation. His mom says "Maybe next Summer." In the very next episode, which takes place in the same Summer, they are going on a "traditional" Summer vacation.
Scenes from a Barbecue - S3-E24
Plot hole: All the kids and Arnie are about to play a basketball game. Darlene and Chuck Jr. battle in Rock, Paper, Scissors to see who picks first. They both throw scissors, and then Chuck Jr. says he gets to pick first. They should have done it over, since that would be considered 'a tie', he really didn't win. (00:12:10)
Plot hole: The mysterious neurosurgeon Dr. Quinn was mentioned by the fake Myles Taggart under the pretence that his presence was announced by the local newspaper. It turns out that his invitation by the university was a lie - presumably no newspaper story existed at all then, or the university would have acted on that. Taggart is exposed as a fraud, Quinn's link to him is so direct that he was even the one who invited him (instead of goading the Colonel into inviting him like it was his own idea) and yet the Colonel continues to trust Quinn blindly - he even has the whole night and day to think about this simple fact, nothing was decided on the spur of the moment.
Suggested correction: Lister can only see M-Corp products and M-Corp employees. Cat is not an employee of JMC or M-Corp, so he disappears. Lister is the only member of the crew who is employed by M-Corp at this point.
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?
Andy Benham ★
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.