Visible crew/equipment: Just before Rimmer sends his 'Internal Memo' Lister is standing next to his fish tank in the sleeping quarters. In the relection of the glass you can see pages being looked through by a member of the crew.
Continuity mistake: At the end of the episode, when the future Lister and the babies appear, Rimmer has his arms folded. In the next shot, Rimmer's hands are on his hips. Also, Lister's locks change positions.
Revealing mistake: When Holly gives Rimmer a new haircut, Rimmer salutes and touches his hair with his hand. Surely he would have noticed his hair has become much longer, especially after he asked for a crew cut.