Visible crew/equipment: When the vending machine says it will destroy Rimmer, a boom mic can be seen at the top of the screen. (00:06:05)

Continuity mistake: Just before Rimmer and Lister drink the hooch, Lister's locks are behind his back, then one of the locks moves to in front of his left shoulder during a brief shot of Rimmer. (00:13:30)
Other mistake: When Rimmer tries to silence the vending machine, he covers up the input microphone with stickers instead of covering the speaker just above it. (00:05:05)
Revealing mistake: When the Cat, Lister and Kryten are walking and the Cat is complaining about rock, keep an eye on the background. They start walking just before a set of steps, then do a complete loop back to the steps for no reason. (00:06:15)

Continuity mistake: When Rimmer gives Hollister the directives to sign, he holds the clipboard in both hands. In the next shot his left hand is under the first page. (00:02:15)
Visible crew/equipment: When we first see Rimmer and Lister in the medi-bay, the camera crew can be seen in the reflection of the tv. A boom mic arm can also be seen moving. (00:16:55)
Visible crew/equipment: After Rimmer faints after getting drunk, a boom mic shadow can be seen on the bedsheets. (00:15:45)

Continuity mistake: When Hollister picks up the lemon drink, his left hand is by his side. In the next shot it is on his chest. (00:01:50)
Answer: Presumably he does, but it's never been used in any material related to the show. He is the only Cat left (as shown in Series 1), so even if he had once had a name, nobody would know it.
Moose ★