Beam Me Up, Scotty!: Say it with me, people. It's "The Answer to the Ultimate Question of Life, the Universe and Everything". Not the meaning of life. It doesn't help that Adams himself wrote a book entitled The Meaning of Liff (defining a number of words that didn't exist in the English language, but should have).
Life Imitates Art: Smartphones and tablets with access to Wikipedia mimic the capability and functions of the Guide with uncanny accuracy.
Life, the Universe and Everything was based on an unused Doctor Who script, Doctor Who and the Krikketmen.note And you can tell: Trillian very much becomes an Expy of the Doctor, with the other characters behaving rather like the Doctor's Companions, although this is in keeping with Trillian's intelligence and generally kind-hearted nature. It might have been a second Hitchhiker TV series.
The later radio series were essentially adaptations of Adams' last three Hitchhiker novels, retconning pretty much the entire events of the second series to being merely the delusional rantings of Zaphod Beeblebrox, instead of following directly from them.
Technology Marches On: Digital watches sure are a neat idea, huh? (In the later radio series, and the movie, they were replaced by mobile phones.)
Unfortunate Name: Slartibartfast. Adams wanted him to have an immense sadness, so gave him a terrible name. He started with FartyFuckBalls, and mutated it until it sounded rude without actually being rude.
Author Existence Failure: Trope Namer, almost; the third book mentions a "total existence failure". Later, of course, succumbed to the trope when Adams died while working on the sixth book; his last published collection of pieces, The Salmon of Doubt, contains an early draft of a Dirk Gently novel that Adams was hoping to rework into a Hitchhiker book.
Creator Breakdown: Regarding the Downer Ending of Mostly Harmless and the mixed-to-negative reaction from fans, Adams conceded, "I just had a thoroughly miserable year, and I was trying to write a book against that background." He intended a sixth book to give the series a better conclusion, but succumbed to Author Existence Failure first.
Executive Meddling: In Life, the Universe and Everything, the Silver Bail of Peace is the Rory Award for "Most Gratuitous Use of the Word 'Fuck' in a Serious Screenplay". US censors were offended, and Adams, bowing to their wishes, promptly changed the offending word to "Belgium". Fortunately, the resulting passage was much funnier, as Adams modified the surrounding conversation to fit the change, as well.
Author Existence Failure: Douglas Adams died a year before the film was completed, though after he'd finished his parts of the script.
God Created Canon Foreigner: Many of the differences from previous versions were Adams creations, from pre-death versions of the script, including the POV Ray, the flyswatters, Humma Kavula, and the romantic elements.
Slartibartfast is not named for the majority of the episode he first appears in. Word of God explained that it was a joke at the expense of the woman who had to type the scripts - that she'd typed this name a dozen times and he simply said 'My name is not important'.
The seventh episode was originally broadcast on 24 December 1978. Consideration was given, partly due to the date and partly due to the fact that all the plot threads had been tied off at the end of episode six, to making it a stand-alone Christmas special in which Marvin would have been both figuratively and literally the star (of Bethlehem), and by participating in a nativity scene would be cured of his depression. In the end they made it a normal episode, devoted to untying enough plot threads for the series to continue.
Casting Gag: The Tertiary, Quandary and Quintessential Phases had a lot of cameos by actors who had featured in non-radio versions of the story:
Chris Langham, Arthur Dent from the 1979 Institute of Contemporary Arts stage production of Hitchhiker's, pops up as Prak in the finale of the Tertiary Phase.
David Dixon, the TV Ford Prefect, had a cameo in the second episode of the Quandary Phase, getting pissed off at Arthur for trying to donate to save the dolphins when he should know they've all vanished. (This case is lampshaded, as Arthur—still played by Simon Jones, who acted alongside Dixon in the TV series—asks if they've met before.)
Stephen Fry, the film's Guide, cameos in the third episode of the Quandary Phase as Murray Bost Henson.
The Quintessential Phase series had Sandra Dickinson, Trillian in the TV version, voice Tricia McMillan (Trillian's alternate universe counterpart).
In a non-remake-related example, Geoffrey Perkins, Douglas Adams's boss at the BBC, plays Arthur Dent's boss at the BBC in the second episode of the Quandary Phase.
Hipgnosis: Did the cover art for the British releases of the soundtrack albums.
Real Song Theme Tune: The theme for the radio show was a snatch of the Eagles' "Journey of the Sorceror", an instrumental from their 1975 album One of These Nights. It would be re-orchestrated for the Radio LPs, and that arrangement was later used for the TV series.
The background characters in the restaurant at the end of the universe are equipped almost entirely with costumes recycled from earlier episodes, and in particular from the various Guide entries, thus helping justify the expense of items which otherwise would have appeared on screen for only a few seconds each.
A badge from one of the Golgafrincham hats would be worn by Arnold Rimmer.