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?
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?
Factual error: Kryten tells everyone that the matter paddle transmits matter in digital form from one place to another at the speed of light - he is very clear on this point. He then locates Waxworld, which is 200,000 light years away. Okay - so when they use the matter paddle to transmit themselves to Waxworld, why doesn't it take them 200,000 years to get there?
Continuity mistake: When Rimmer leaves for his exam, the table in the room only has an ashtray on it. Moments later, when Lister locks the door, a magazine, a can and a mug have appeared on the table. (00:14:30)
Visible crew/equipment: When the Cat says "You mean to help you get out if the program freezes" on Blue Midget, a soundman can be seen crouching behind the control panel. The top of his head is visible in the top right of the screen. (00:14:10)
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)
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.
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)