Other mistake: When Lister reads Rimmer's diary, he reads the first entry, then his aunt's birthday in July and then the entry for Gazpacho Soup Day in November. Each time he looks for the next entry he flicks though the pages, yet every time he reads, it is from the start of the diary. (00:15:25)
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.