Other mistake: The tax letter and Rimmer's mother's letter are both already opened before Lister takes the letters out. As there is no one else aboard Red Dwarf, the letters would not have been checked by anyone so they should still be sealed. Also, not all of the letters are already open, just the two that Rimmer receives.
Suggested correction: Unfortunately, we aren't provided with enough information about the envelopes Dave didn't open to determine if they were all unsealed or not. Maybe all JMC post is opened and checked before being put in the post pod. That way, any potential threat is identified before the pod gets on board the ship, which seems a sensible security measure.
Other mistake: The shots of Blue Midget driving back to Red Dwarf that are shown from behind are visibly the exact same shots used each time. This is evident as the driving movements of Blue Midget, its position in the frame, and Red Dwarf's position in the background are all identical each time.
