When Ford and Arthur are in the pub, there is an outside shot of the pub illuminated by a low evening sun; whereas in other outside shots, and on the pub clock, it is clearly nearer mid-day with bright sunshine.
When explaining why he needs one, Ford hands the towel to Arthur twice.
The Red Lion's barman pulls six pints of Tamplins bitter in the physically-impossible time of under twenty seconds from Ford ordering the round.
When The Book is reciting the information about Vogons, it says "subjected to public enquiry, lost again, and finally buried" but the text on the screen says "subjected to public enquiry, and finally buried".
While Ford and Arthur are walking away from the bulldozer, a film crew vehicle can be glimpsed over the fence behind them.
Arthur cannot understand Vogon speech until he has had a Babel fish inserted in his ear by Ford, but minutes earlier the people of earth screamed in understanding of the Vogons' message of impending doom. (This same plot hole is present in just about all versions of the story.)
Several characters incorrectly describe the Vogon ships as saucer-shaped.