Other mistake: The tax letter and Rimmer's mother's letter are both already opened before Lister takes the letters out. As there is no one else aboard Red Dwarf, the letters would not have been checked by anyone so they should still be sealed. Also, not all of the letters are already open, just the two that Rimmer receives.
Other mistake: The shots of Blue Midget driving back to Red Dwarf that are shown from behind are visibly the exact same shots used each time. This is evident as the driving movements of Blue Midget, its position in the frame, and Red Dwarf's position in the background are all identical each time.
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.