Revealing mistake: When the two Rimmers are exercising, there are no stars visible out of their window. (00:11:20)
Revealing mistake: When Lister goes to Rimmer's room the second time, the door opens before Lister hits the switch.
Revealing mistake: When Holly is talking about his chess game, you can see his black clothing to the left of his chest, revealing he's hiding a body, and isn't just a computer generated floating head. (00:06:30)
Revealing mistake: In the observation dome, the borders of the blue screen used to project the image of space behind Lister and Rimmer can be seen around the dome. (00:09:55)
Revealing mistake: When Lister and Rimmer are talking in the dome, the machine behind Rimmer keeps wobbling. (00:09:55)
Revealing mistake: In the observation dome, background stars are visible on Lister's hair and neck. (00:10:05)
Revealing mistake: When the Outland Revenue guy breaks Rimmer's thumb with the mallet, the mallet does not touch his thumb, but instead his fingers. (00:28:35)
Revealing mistake: Holly's night cap is in front of the edges of his monitor. It should fade into the white border of his screen. (00:05:25)
Revealing mistake: During filming of the this episode, Craig Charles was called away for the birth of his son, Jack, so production manager Mike Agnew stepped in. Although Lister is wearing a space suit at the time you can still tell which part is Mike thanks to a continuity error - Mike forgot to put on Lister's plaster cast. (00:15:15)

Revealing mistake: When Lister uploads his memories, the wide shot shows various videos of Rimmer in the background, but in the close up it shows a plain white screen. (00:17:55)
Revealing mistake: The square bluescreen outline can be seen in the wide shot of the obervation dome scene. (00:24:50)
Revealing mistake: When Rimmer and Lister are in the observation dome, background stars can be seen on Lister's locks and on the top of his forehead. (00:25:40)
Revealing mistake: When Lister and the Cat drop the gravestone and break their feet, you can see that it does not land anywhere near Lister's left foot. (00:26:55)
Stasis Leak - S2-E4
Revealing mistake: In the opening, Holly gives an additional message saying "On our journey, we have encountered many strange and bizarre things. Only last month, we can across a moon which was shaped exactly like Felicity Kendal's bottom. We flew around that one a couple of times." Before Holly says "We flew around that one a couple of times", he can be seen about to say the line, but visibly hesitates, presumably waiting for his cue. (00:01:35)
Stasis Leak - S2-E4
Revealing mistake: When Lister, the Cat and Rimmer are stood in the shower and the Cat keeps saying 'What is it?' he turns to Rimmer and brushes against his tie throughout the scene. (00:10:05)

Stasis Leak - S2-E4
Revealing mistake: Rimmer, Lister and the Cat are not visible in the mirror when the crew member finds them in the shower. (00:10:25)
Answer: The cello is a large four-stringed instrument, which, when it is played, stands vertically on the floor between the player's legs (assuming they are seated). If it is to grow as large as the other instuments mentioned will, it would require a rather unseemly lack of femininity to be able to encompass it with the legs.
Rooster of Doom