Revealing mistake: When Rimmer stands up from underneath the table, just before he says, "Thanks for your support" to Lister, listen very carefully and you can hear the stunt director saying "Action!" backwards. This shot was the splice point between the reversed and the regular footage. (I know this mistake is listed as being in the 'backwards version' on the DVD, but it is in the regular broadcast version too - you just have to listen harder for it.)
Gunmen of the Apocalypse - S6-E3
Revealing mistake: At the start of the episode, we see Lister in black and white talking to Loretta. Then we cut back to what's really happening, he is playing on the AR console. Look at the door behind him, you can see Kryten's hand sticking out in the doorway. He is supposed to rush in and start talking, but you can see him waiting off camera to be told when to enter the room.
Revealing mistake: When Lister and Cat are in Starbug searching for Rimmer and Kryten, the background of space shown out the window remains entirely still and doesn't move. (00:11:15)
Revealing mistake: The scene where the pub manager comes backstage to yell at Rimmer and Kryten was filmed, and then reversed to appear as if he was yelling backwards. Rimmer blinks when he is being yelled at, and due to the scene being played in reverse, his facial movements appear reversed, even though he is supposed to be moving forwards. (00:22:00)
Revealing mistake: Lister and Cat get a ride to Nodnol after a man they bump into offers to take them in his van. The logo on the van appears completely normal, and has not been reversed, even though everything in this version of Earth is supposed to be reversed. (00:16:15)
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.
Confidence and Paranoia - S1-E5
Revealing mistake: When Confidence is trying to get Lister to take his helmet off, Lister climbs over a railing and jumps around him. It is clear that the footage of Lister jumping around was slowed down to make his movement appear as if there is a lack of gravity. (00:26:35)
Revealing mistake: When Rimmer and Lister are being forced out Captain Hollister's office due to the effects of the fight catching up with them, a rattling sound can be heard off-screen, indicating the use of a hidden trolley-like device pushing them into the wall. (00:21:55)
Revealing mistake: When they change Professor Edgington from ape form to human form, the human form is obviously a lifeless mannequin. (00:23:35)
Revealing mistake: As Lister tries to sharpen/shorten his nails after getting out of deep sleep, you will see just before he stops that one nail snaps at the finger. He continues as if nothing happens, holding his hand still, as if it was still in the sharpener. (00:02:00)