Revealing mistake: When the cat priest dies on the bed, watch him move his foot so Lister can sit on the edge. (00:26:40)
Visible crew/equipment: When talkie Toaster says, 'I toast, therefore I am.', you can see the legs of a crew member moving in the reflection of the toaster. (00:04:40 - 00:11:50)
Continuity mistake: Watch the cat priest's black hand. It starts off normal, then it turns crusty and white. Just before he dies, his hand is normal again. (00:25:55)
Other mistake: In the picture of the cat wars between the Red Hats and the Blue Hats, the hats are orange instead of blue. (00:19:00)
Continuity mistake: After Rimmer and Lister argue about the pod, Rimmer walks off and Lister steps into the observation room. As Lister steps in, his locks are over his left shoulder, then in the next shot they are over his right shoulder. (00:14:05)
Revealing mistake: When Rimmer wakes Lister up, as he stands up you can see he moves Lister's duvet with his shoulder, which he can't do, being a hologram. (00:15:20)
Continuity mistake: When the cat priest dies, the hat he is wearing falls onto the bed above his head. When the shot changes the hat is gone. (00:26:35)
Continuity mistake: When Rimmer says he wants the 'aliens' to give him a real body, his arms are outstretched. In the next shot they are folded. (00:17:20)
Continuity mistake: When the Cat leaves Lister's quarters after showing him the cat book, one of Lister's locks is hanging over his right shoulder. In the next shot it is gone. (00:11:40)
Other mistake: The Cat Priest has no fangs when every other Felis Sapiens has them.
Visible crew/equipment: When Lister steps back inside the observation room after Rimmer leaves, a stage light can be seen reflected in the window-like light fixture on the wall. It can't be a light on the ship as none of the lighting on Red Dwarf is in the shape of the light seen in the reflection. (00:14:05)
Continuity mistake: When Rimmer first realises that his files are unflattering, the screen first from the right on the computer bank shows writing. But a change of view later, Holly is on the same screen. He does not have time to move.
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 ★