Continuity mistake: When they're trying to choose which portal to go through, watch the pattern on the ground. From shot to shot it's either covered by snow, partially visible, or completely exposed, with no time for the wind to blow the snow around. (01:14:15)
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. (01:27:55)
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: When Ford is drinking in the bar, the amount of beer in his glass goes down mid-drink.
Continuity mistake: When Humma Kavula holds up the IID coordinates, his grip on the chain changes between shots.
Continuity mistake: When Marvin is holding the point of view gun, there is an empty space behind him where Arthur's caravan was a moment ago.
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: 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.
Continuity mistake: When Arthur reattaches Marvin's arm, the black rubber shoulder joint is nowhere to be seen.
Factual error: If the Vorgon Destructor Ship was as massive as portrayed, then as Ford and Arthur look up at it, it should have been reflected in Ford's shades. Instead, all that is seen is the demolition equipment and open sky.
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.
Continuity mistake: When Trillian tells Arthur about the machine that makes you whatever you crave, she gets a donut on a plate and it is perfectly visible when she gets out the saber knife, but right after she cuts the toast-bread it has disappeared.
Chosen answer: Because it was a radio show originally, Douglas Adams would write broadcasts from show to show. He did not know where something would lead, which let the plot become random and funny. So ultimately it was originally created to be funny, then he found a way to link it back in later.