These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
The most egregious being Zaphod's second head, a mechanical prop which barely functioned and veered right into the Uncanny Valley.
What the Hell, Casting Agency?: Trillian's accent. Seriously, what the Belgium was that all about? Made even stranger by the fact that she could do a perfectly passable English accent, as seen on a few outtakes. Apparently she asked Douglas Adams if he wanted an English accent, and he was so happy with her casting in the first place that he said no, she should use her normal voice. He came to regret this, in part because he realised it wasn't a particularly flattering thing to say to an actress.
The video game:
Blatant Lies: Ford's claim to be from Guildford becomes this since he's got an American accent, unless one is supposed to believe he means he's from America via Guildford.
That argument only works if you're British and you're thinking of Guildford, near London. This film was made for Americans, who will think first of Guildford, Connecticut (just down the road from New London CT, oddly enough). A black American from Guildford is perfectly feasible - so long as the Guildford is in New England.
There is also a Guildford in Vermont and a Guilford County and town in North Carolina. So lots of places for an American-accented Ford Prefect to come from. Only... the American version might have renamed him "Ford Edsel" or something, as the Prefect was only ever sold in Britain?
Mis-blamed: Many things the fans complained about were Adams' intention from when he first outlined this adaptation - fans should remember that he tried to work in new bits into every new Hitchhiker's adaptation - and much of the script was written by him.
Older Than They Think: Some people think that the movie ripped off the name "Babel Fish" from the now-defunct translation website, completely forgetting of course, that it is in fact the other way round considering the source material. The name itself, meanwhile, is in turn based on the biblical story of the "Tower of Babel".
One-Scene Wonder: Humma Kavula. Whether you approve of his addition to the story or not, there's no denying that John Malkovich (with the help of the special effects team) makes him a memorable character.
Romantic Plot Tumor: This very movie features a fairly obvious example of this trope, between Arthur and Trillian. The "original" source materials (book, TV and radio series) all handled their past differently, but agreed that Arthur had been briefly interested in Trillian during a single superficial encounter in the past; when he re-encounters her during the story, he displays jealousy at a few points, but not much more than that. By comparison, the movie version features an Arthur who is desperately pining over Trillian, who could have been his one true love had he not been afraid to pursue her, and he spends most of the movie time thinking about, worrying about or focusing on her. This was deliberately inserted by Douglas Adams when drafting the movie, before his death, to increase studio interest and audience acceptance of the movie.
Actually, he tried to work it into the television adaptation, but the chemistry wasn't there between the actors.
Unfortunate Implications: Trillian insisting that the Point Of View gun won't work on her because "I'm already a woman." Yeah, there are several attempts by fans to explain that one away, but it still sounds rather iffy.
The franchise in general
Adaptation Displacement: Most people are familiar with the series as either a five or six book "trilogy", unaware that it was first a radio program. For those people who know about the radio series, this makes the complaints of the book-only fans about the 2005 movie absolutely hilarious. Also, many fans get the timeline backwards on the novels and the radio series (the novels are the adaptation).
Angst? What Angst?: Trillian barely notices when her home planet is blown up and billions of people are killed. Dent has the decency to be shocked for a few minutes, though once he realizes that he can't quite wrap his head around the magnitude of the loss he starts going into culture shock.
Film version Trish Mc Millan doesn't even find out until late in the story thanks to Zaphod. When she find out, she goes ballistic.
Common Knowledge: 42 is not "The Meaning of Life", it's "The Answer to the Great Question of Life, the Universe, and Everything." The reason it seems so random and nonsensical is because it's only an Answer, and no one actually knows what the Question is.
Continuity Snarl: Adams deliberately ensured that no two forms of the franchise were the same, with the exception of Arthur and Ford fleeing the Earth in Fit/Chapter/Part One. In a sense, Adams was Trolling his own fans... or at least making sure everybody remembered the MST3K Mantra. Which would you rather do, bicker over fictional minutia or have a good laugh?
Mis-blamed: Many people actually cry Adaptation Decay or They Changed It, Now It Sucks to the various adaptation(s) because they're "not like the book". This is despite that Adams actually approves them himself (and is pretty much involved in the production of them all, see in the movie section.) and he's stated, numerous times, that he wanted them to be different. Plus, it overlooks the fact that the books themselves were an adaptation. And that Hitchhiker's Guide has always changed drastically between incarnations.