"Fan" is a misnomer, but readers of the aforementioned blog by Fred Clark have made a running joke on Slacktivist of referring to Carpathia as "Nicky (insert mountain/mountain range name here)"; recently, a new nickname, Chairface Carpathia, seems to have caught on. Buck, the Greatest Investigative Reporter of All Time, is called the GIRAT. The authors (LaHaye and Jenkins) are often abbreviated to "Ellenjay".
"Meta-(character)" is frequently used by the same community used to describe any character who seems to be showing signs of behaving like an actual human being in the actual situation they are currently in. This title often confers a sort of temporary Ensemble Dark Horse status as well.
Parody: The book Right Behind and its sequel Supergeddon poke fun at the book series.
Technology Marches On: You can tell how old the earlier books are by their lack of cell phones and their ilk. In the written-in-2005-and-2006 prequels, though...
The updated version of the series updates the technology to later standards: VCRs become DVD players, CD players become iPods, cassette recorders become MP3 recorders, etc.
A telling moment of this is in Chapter 12 of the first book, which mentions a video recording of a sermon about the Rapture that Rayford has watched. Apparently, the rewrite missed a pretty crucial use of the word "VCR":
"He also wanted to plead with her to watch the DVD [...] He had rewound it and left it in the VCR, hoping and praying she would watch it while he was gone."
Unless Rayford was dumb enough to buy a DVD rewinder...
Word of Dante: The fan community has somehow decided that Cendrillon Jospin of Kingdom Come is a space geek.
California Doubling: Toronto as New York for the 2000 movie. If you look closely, the international flags displayed at the UN are actually those of Canadian provinces. Also, the scenes in Israel were shot in a quarry in Ontario.
Creator Backlash: Original series' authors Tim LaHaye and Jerry B. Jenkins were far from happy with the finished product, as it had been originally pitched to them as a big-budget, mainstream blockbuster described as "the biggest and most ambitious Christian film ever made", rather than the low-budget, direct-to-video adaptation it became. LaHaye even went so far to sue the production company, and was quoted as saying; "My dream has always been to enter the movie theatre with a first-class, high quality that is grippingly interesting, but that is also true to Biblical storyline, and that was diluted."
Dawson Casting: In the first Left Behind film (which came out in 2000), Chelsea Noble was in her mid-thirties, playing 27-year-old Hattie Durham. Janaya Stephens was 27-years-old at the time, playing 20-year-old Chloe Steele. Gordon Currie was also in his mid-thirties at the time, playing 33-year-old Nicolae Carpathia.
Disowned Adaptation: Tim LaHaye and Jerry B. Jenkins, the authors of the Left Behind series, hated the adaptations by Cloud Ten Pictures, calling them "church basement movies" and going so far as to sue the studio (and win) over it. As a result, their names are not listed in the opening credits of the first film, even though it still lists the novel as the source material. This is a big part of the reason why the film series was rebooted.
The Other Darrin: In the first two movies, Bruce Barnes was played by Clarence Gilyard, Jr., before being replaced by Arnold Pinnock, as due to scheduling conflicts, Gilyard was unable to reprise his role as Bruce in the third movie. That and since Gilyard is a Roman Catholic, his priest was slightly peeved about him taking the role, given the series' stance on premillennial rapturist theology (i.e. a belief held by Protestants, not Catholics), and was very happy when Gilyard did not reprise the role.
Troubled Production: Producer Ralph Winter (of X-Men Film Series and Star Trek fame) and writer Alan B. McElroy (the co-creator of Spawn) were attached to the project early on, envisioning a high-concept, mainstream blockbuster that won over series authors Tim LaHaye and Jerry B. Jenkins. The two ended up leaving the project in pre-production, though their names are still listed in the credits, at which point it was passed on to brothers of Paul and Peter LaLonde of CloudTen Pictures, who retooled it as the low-budget, direct-to-video fare that it ultimately became. Needless to say, LaHaye and Jenkins were far from happy, the former going so far as to sue the production company for misleading them as to the nature of the film, and both Winter and Elroy quietly disassociated themselves from the property.
Real-Life Relative: Inverted, as Kirk Cameron (Buck Williams) and Chelsea Noble (Hattie Durham) are married in real life, having met on the set of Growing Pains.
Ironically, Kirk Cameron admitted that his wife had pictured a movie adaptation in her mind with the both of them as Buck and Hattie respectively shortly after completing the first book. Several weeks later, Cameron was notified of the movie adaptation and was tapped for the role of Buck Williams. He got the part of Buck, while Chelsea Noble claimed the role of Hattie.
Wag the Director: As mentioned on the trope page, Kirk Cameron did not grow out of this after Growing Pains. In Left Behind: Tribulation Force, there's a scene which has Buck Williams (Kirk's character) and Rayford Steele confronting a friend of the latter who didn't want to hear what the Antichrist planned to do. Cameron (who by that point had just teamed up with Ray Comfort's "The Way of the Master" ministry) manages to combine this with a Big-Lipped Alligator Moment when he suddenly throws in this random string of questions related to the 10 Commandments lifted almost word for word from a "The Way of the Master" video he appeared in.
Creator-Preferred Adaptation: LaHaye and Jenkins both gave the 2014 version high marks, with LaHaye even describing it as "the best movie ever made about the Rapture".
Stillborn Franchise: From the looks of it. The ending of the film obviously sets up for a sequel and the creators started pitching for oneon Indiegogo in April of 2015, hoping for a release in the summer of 2016. However, by the time the crowdfunding campaign ended a month later, it hadn't come close to its $500,000 goal. The film's website hasn't been updated since, leaving the future of the film unclear.
As of July 2017, Peter Lalonde, producer of the 2000-2005 films, announced plans to film all 16 books.