Character mistake: Rimmer asks Kryten to make the new computer blonde. When the computer launches, the computer's hair is brunette. (00:07:30 - 00:08:45)
Other mistake: An option for the new computer is breast size. A meaningless addition, since the computer is just a head. (00:07:35)
Suggested correction: When setting up the computer, there is an option for frame size. Kryten chooses close up, and when Pree appears on-screen Rimmer reacts to the fact that her breasts aren't visible whilst Kryten says that he likes that frame size. Presumably, there were other frame sizes available that would reveal more of Pree's body, giving meaning to the option.
Deliberate mistake: When the computer has been launched, Lister walks into the drive room and notices the computer and stands behind Kryten and Rimmer. But when the camera is focused on the computer, there is no sign of Lister what so ever. (00:10:00)
Continuity mistake: When Lister notices the video, the silhouette of a flashing blue light is cast on the table (to the left of screen). In the next shot, there is no sign of the flashing blue light. (00:10:40)
Revealing mistake: When Pree shows Lister his Medi-Bay file, it is a flipped shot. Note the danger sign next to the computer. (00:27:40)
Audio problem: When they are chasing Jesus through the market, Lister's mouth is out of sync when he's shouting. (00:26:15)
Character mistake: Upon hearing that Lister, Kryten, Cat and Rimmer have travelled from Albion - England - to India the woman in the market expresses surprise that they have travelled "halfway across the known world" just to buy lemons. In 23AD travelling from England to India was all the way across the known world. The Americas, Australasia and China were completely unknown at the time.
Character mistake: Surely, a know-all like Kryten would know that although lemons are not native to the Middle East, Babylonian traders imported lemons into what was then Judea some five hundred years before Christ was born, and by 4BC, they were quite common in the area, albeit as a pricey imported delicacy. The Dwarfers wasted half of their epic overland trek.
Factual error: At the very end of the episode right before the Dwarfers sees Jesus and Judas, there is a plastic cup on their table. The episode is set in 23 AD.
Revealing mistake: When they change Professor Edgington from ape form to human form, the human form is obviously a lifeless mannequin. (00:23:35)
Continuity mistake: When the book "Roots of Coincidence" is first seen it's a paperback but later in the episode it's suddenly a hardback.
Visible crew/equipment: When Rimmer and Kryten invites Snacky to come with them to Red Dwarf, the reflection of a crewmember is visible in Snacky's head dome. (Note this is not Rimmer's reflection since there is no H).
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.
Other mistake: When Cat picks up the can of Leopard lager which is invisible to Lister, he shakes it, pops the cap and sprays Lister with foam. The foam is visible but the can remains invisible, and that makes no sense. If we are seeing the scene from Cat's point of view the can and foam should both be visible, and if it is from Lister's then neither should be.
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.
Continuity mistake: Rodon is revealed to be the Cat's older brother, and the rebelling cats refer to the Red Dwarf itself as the ship of their birth, but in Psirens, it was revealed that the crew spent 200 years in deep sleep while tracking Red Dwarf. This appears to have been forgotten.
