Revealing mistake: After the crew transport themselves out of the book depository to escape the FBI, the astronaut helmet is transported afterwards and the two FBI agents start shooting at the box the helmet was placed on. When the box is shot, there are no bullet holes left on it.
Timeslides - S3-E5
Factual error: The newspaper detailing the bomb attack on Hitler lists the date as "Tuesday May 4 1938." May 4th, 1938 was a Wednesday. (00:09:15)
Revealing mistake: When the Polymorph, posing at the snake, jumps on Lister, it is apparent that the snake on Lister has been replaced by a plastic inflatable replica that has no features and does not move. (00:10:05)
Continuity mistake: When the Cat is eating the food set out by Lister, there is a cloth on the table. When Lister is asking where the other kitties are, the cloth is shown near the centre of the table. Rimmer then says he wants it off the ship, and the cloth is suddenly further to the right of the table. (00:27:45)
Continuity mistake: When Lister is revising for the exam, he opens a can of beer which sprays foam onto the table, and onto his cigarettes, when he opens it. A few seconds later, the sprayed foam disappears from the table. (00:19:30)
Continuity mistake: When Rimmer is talking to Lister before the exam and says they are friends, Lister replies "When?" Lister has a can of beer on the bunk, with the label facing the camera. Two shots after, the label is suddenly facing away from the camera. A couple of shots after that, the label is suddenly facing the camera again. (00:23:15)
Confidence and Paranoia - S1-E5
Continuity mistake: When Confidence is telling Lister that his song was the greatest love song ever, Lister has his right hand on his lap, but in the next shot, his right hand is suddenly on the guitar strings. (00:19:35)
Continuity mistake: When Lister is questioning how they can remake Casablanca, he is holding the video tape, but in the next shot, the tape has disappeared from his hand and is touching the control panel. (00:04:40)
Continuity mistake: When Lister is getting ready, he pulls his trousers off the table, causing the boot on the table to wobble. In the next shot, the boot is entirely still. (00:10:35)
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)
Continuity mistake: When Rimmer falls asleep whilst Lister is doing the jigsaw, there is a whisky bottle on the table. Later in the episode, when being viewed on the black box, the whiskey bottle is no longer on the table. Lister could not have thrown it away since he left the table to the Hologram Simulation Suite at The End of the scene. (00:10:20 - 00:19:35)
Continuity mistake: When Lister is doing the jigsaw and Rimmer starts singing in bed, the pint mug on the table has nothing in it. Later on, when Lister returns after giving Rimmer his memory, an inch of whisky has suddenly appeared in the bottom of the mug. (00:10:20 - 00:19:35)
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)
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)
Revealing mistake: The potatoes used in spud duty are obviously just cardboard cut outs used to give the impression that there are lots of potatoes. (00:19:25)
Revealing mistake: When Rimmer runs to Lister after Lister unsuccessfully orders a black coffee, the camera tilts.
Revealing mistake: When Lister goes to Rimmer's room the second time, the door opens before Lister hits the switch.
Timeslides - S3-E5
Other mistake: In S2 E2 Better Than Life, Rimmer mentions that his brother Frank was 6' 5" by the time he was 11 due to their father pulling him on a tractor, however in S3 E5 Timeslides, the picture of Frank Rimmer's wedding shows Frank to be of fairly average height, and not 6' 5".
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.)
Stasis Leak - S2-E4
Continuity mistake: When Petersen walks away from Lister with the cases, the two women follow him. In the next shot the women have swapped places. (00:17:45)
Answer: It's Queen Victoria, someone any Englishman would recognize, and needed no introduction.
Kryten was introducing the "people" to Rimmer. Rimmer isn't an Englishman; he's not even from Earth; he's from Io.