Continuity mistake: When Arthur breaks the arm of the chair as his brain is being taken, the arm is strapped to his wrist. A second later the strap and broken arm are gone.
Visible crew/equipment: When Ford runs past the caravan to chase the Vogons with a towel, you can see the cameraman, and about 4 other crew members reflecting in the caravan's surface.
Continuity mistake: In the scene where Arthur is lying in front of a bulldozer, he is so close that his hand is touching it. Two shots later he is a foot away from it, without appearing to have moved at all.
Other mistake: In the opening song, the dolphins sing: "If we could just change one thing, we would all have learned to sing", however the subtitles on the DVD say "lungs to sing". As a side note, dolphins do indeed have lungs.
Visible crew/equipment: On the DVD version, in the scene where Slartibartfast is taking Arthur to his home with the "air lift", when over the fields of England, on the bottom left corner you can see the shadow of the helicopter with which the aerial footage was shot.
Continuity mistake: When Arthur Dent is seen at the start of the film in his house and the table starts to vibrate (due to the demolition team outside), the table seen in the background does not vibrate at all.
Continuity mistake: When Arthur reattaches Marvin's arm, the black rubber shoulder joint is nowhere to be seen.