When Arthurs' home is about to be demolished, he is seen lying on the ground in front of the bulldozer in protest. His left arm is touching the scoop of the bulldozer. The shot cuts away and directly back to him, at which time he is lying 1 to 2 feet away from the scoop of the bulldozer.
When Ford is running to rescue Arthur and the gang as they are being shot at outside Humma Kavula's temple, Ford starts running to the rescue and is supposedly screaming but his mouth is clearly closed.
When Marvin and Arthur are sitting by the inter-dimensional portals, Marvin mentions he is a "manically depressed robot." This not technically correct, as manic depression - aka bipolar disorder - is characterized by two extremes in behavior: sadness, lethargy, hopelessness, etc. (what Marvin displays); and mania - which is usually excessive activity (doing a lot of things at once) and sometimes happiness. Marvin did not really show mania.
Dent's "Best laid plans of mice and men" is a common misquote. It should be "The best laid schemes o' mice an' men" and the full quote is "The best laid schemes o' mice an' men, Gang aft a-gley," from the Robert Burns poem "To a Mouse," written in Scottish dialect. Translation: the best laid schemes of mice and men often go wrong.
When Ford is scooting along with the trolley full of beer he passes a red truck on the right side of the screen (Ford's left side); however, when the shot pans out there are only red trucks on the left side of the screen (Ford's right).
When the mice say "To business!" (in the last scene at Arthur's house), the teacup is not in the saucer. Although Arthur drinks from it once more and puts it down, it never appears in the saucer again.
In front of the portal on Magrathea, there is snow on the ground then Trillian goes through the portal and some snow is blown away, revealing tiles on the ground. Ford runs into the portal and suddenly, more tiles are revealed for no apparent reason. Change camera, the tiles are covered and Zaphod enters the portal. Change camera, many more tiles are exposed.
The goof item below may give away important plot points.
When the brain extractor rises from the fruit bowl, most of the fruit falls off but a red apple stays on. As the camera change to Arthur and then back to the mice on top of the extractor, the apple rotates. As the camera snaps to a wider view and the saw blades extend, the apple falls off but has been rotated again.