Continuity mistake: From the model shot of Blue Midget, Kryten is seen sitting on the right. When the camera cuts inside the ship, he is sitting on the left. (00:22:40)
Suggested correction: When the exterior shot of Blue Midget is shown, it is not very easy to tell the crew apart. They appear blurred, so it is impossible to determine who is sitting in which place.
Other mistake: When Lister inadvertently sets off the Auto Destruct sequence, the computer voice says the ship will detonate in 15 minutes. The computer then says "the ship will detonate" every five seconds followed by how much time until detonation, but the time in which the computer says this is inconsistent. Two seconds after the computer says 15 minutes, the computer says the ship will detonate in 14 minutes 55 seconds. Ten seconds after saying that, the computer says the ship will detonate in 14 minutes 50 seconds. (00:01:50)
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.
Other mistake: The Cat Priest has no fangs when every other Felis Sapiens has them.
Suggested correction: How is this a mistake? It isn't known that every Felis sapien from 3 million years of evolution must have fangs.
Other mistake: Cassandra says that all the canaries will be dead in 1 hour, with the exception of Rimmer, Kryten, Lister, Cat and Kochanski. However, Kill Crazy was still knocked out in the transport vehicle and presumably would have survived too.
Suggested correction: But Cassandra was known to lie if it suited her purpose, she said that Lister would harpoon Arnold through the head and kill him but that's not what really happened either.
Yes, Cassandra lied about Lister shooting Arnold through the head with a harpoon, but that was an attempt to stop Lister from killing her. Mentioning which of the canaries will survive had no impact on any of her plans, so not mentioning Kill Crazy survived is still incorrect on her behalf.
Revealing mistake: After Starbug has left Red Dwarf, the scene cuts to inside the ship where Rimmer tells Kryten to autopilot, and the background of space is entirely still, even though the ship is moving. (00:04:45)
Suggested correction: Stars are so far away that they do not appear to move when travelling in space, unless you reach incredibly high speeds or change direction.
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.
Other mistake: When the Cat says there better be no dogs on the ship, there are only about two or three stars visible out the window. Far too few given the amount of stars shown in exterior space shots of the ship. (00:05:15)
Suggested correction: They aren't stars; it's dust on the window... (a reference to a later episode).