Dawson Casting: Michael York was already 33. Jenny Agutter was 24, playing a 17-year-old. The main reason the death-age was raised, from 21 in the novel to 30 in the movie, was because the actors chosen to play the roles could never pass as teenagers. Richard Jordan (Francis 7) was 38 years old during filming. This also bypasses issues with the limited hours younger actors can work — not to mention the uncomfortable implications for some of sexually-active 14- and 15-year-old "adults".
Executive Meddling: The powers that be insisted that many important scenes be cut so the result would be rated PG. The 'Love Shop' sequence ran about four minutes, and featured more nudity. Likewise Box would make a nude ice sculpture of Logan and Jessica. Another sequence of characters visiting the "Hallucimill" shop in Arcade was cut for its depiction of drug use. The footage is considered lost nowadays.
In the final scene when the crowd is gathering in awe around the Old Man, one of the extras gives the Vulcan salute that is of course familiar from Star Trek. The director probably either didn't recognize it or didn't mind it in the least. At the time this film was made, Star Trek was still just some obscure cancelled TV show from The '60s and had yet to catch on with the general public. It wouldn't have its own official revival until three years later.
Peter Ustinov improvised most of his dialogue on set. He also used US pennies for the buttons on the Old Man's costume, because he apparently couldn't find any real buttons.
Logan's black house robe was thrown together in about two hours while the set was being lit. The director spontaneously decided that Logan should look more casual in his apartment on the first day of shooting.
When the Old Man is showing Logan portraits that used to hang on the walls of the Capital, he was going to show one of Richard Nixon - and say "they used to call him tricky...something". The gag was dropped because it was considered too controversial at the time.
All the costumes were going to be much skimpier on all the characters. This idea was eliminated because having to apply make-up on so many extra body parts would have cost too much.
The Cat Fight between Jessica and Hollie was much longer, but the actresses got so into it that the director changed it out of fear that they would legitimately hurt each other.
Morgan Woodward played Morgan, the leader of the Council of Elders.
Lisa Eilbacher played Lisa in "The Innocent".
Executive Meddling: CBS asked to have the pilot re-shot to include the Council of Elders ruling over the City of Domes, which not only completely changes the concept of the original film, but in introducing the elders, Francis' entire motivation for pursuing Logan and Jessica is changed (in the TV series, he's clued into the true nature of the city and "renewal" and is offered a seat on the council - and life beyond age 30 - if he successfully captures the two alive).
Follow the Leader: Inverted. The TV series was in the works before Star Wars came out. But since it didn't appear until after, it just looked like a knock-off, which is ironic given the original film it was based on predated Star Wars by a year. (The "follow the leader" effect might have been worse had the episode "Turnabout", which included a duel with electric swords that sounded just like lightsabers, been broadcast in 1978, but the series was pulled from US airwaves before it aired. (It was shown internationally and is included on the DVD set.)
The episode "The Collectors" predicts both e-books and PDFs.
The episode "Turnabout" predicted by decades the current issues and debate over some religions and cultures requiring women to cover their face.
Missing Episode: The last three episodes never aired in the US, due to the show being cancelled. They aired in the UK and finally on TNT in the 80s when Ted Turner bought the MGM library.
The Other Darrin: No one from the original film carried over to the series. Only three characters were retained: Logan, Jessica and Francis, with Jessica given the same hairstyle and general appearance as Farrah Fawcett's character in the film. Although the film did include a robot character named Box, Rem is a completely different (and far more benevolent) character.
Dorothy Fontana, David Gerrold, and several other Star Trek alumni were involved, and the Trek influence shows up heavily in some episodes like "Fear Factor".
Many people who worked on the series were later involved in Dallas, which began shortly after Logan's Run was cancelled, including the producer Leonard Katzman, the writer D.C. Fontana, the directors Robert Day, Irving J. Moore and Michael Preece and actors such as Donald Moffat, Randy Powell, Morgan Woodward, Jared Martin, Sherril Lynn Katzman, Mel Ferrer, Liam Sullivan and E.J. André.
Recycled: The Series: Saul David and MGM studios had no dreams of a TV series when they were filming the movie. Some of the props were re-used for the series. The pilot episode (and opening credits) reused special effect footage from the film - most notably the Carousel sequence and the model of the City of Domes, and its first act is a (very) condensed retelling of the original film story. A later sequence in the pilot introduces a character named Martin who is clearly intended to be an Expy of Peter Ustinov's old man; some of Jessica's dialogue towards the character is paraphrased.
Screwed by the Network: Early ratings were very strong, but CBS kept changing the schedule, disrupting the viewers. It was cancelled after only eleven episodes.