Plot hole: Lister and Kryten seem to know about Cassandra's prediction that Rimmer would sleep with Kochanski despite the fact that they were not there when Cassandra said it. (00:25:15)
Suggested correction: Rimmer told them, just not on screen.
Plot hole: Lister is not allowed any dangerous objects that he might try to commit suicide with, yet when he is with the canaries on their missions, he carries an assault rifle. The canaries aren't always supervised and it would be impossible for a guard to stop any of them putting a gun to their head and pulling the trigger. (00:05:05)
Suggested correction: We only hear from Rimmer that that's a rule. Rimmer is usually wrong about most things.
Plot hole: Pete the sparrow was dead before the time wand was used on him to become a dinosaur. When the undo button was pressed, Pete should have turned back into a dead sparrow. (00:23:10)
Suggested correction: Unless the "undo" time on the wand was set to shortly before he died, it isn't explained exactly how the wand works or what the control options are, so it's possible.