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."
Actor Allusion: In the third movie, President Fitzhugh is played by Louis Gossett, Jr. His other presidential role was that of Anwar Sadat.
The Danza: Kirk Cameron playing Cameron "Buck" Williams.
Subversion; Williams was named well before Kirk Cameron got the part, since the book came out well before the movie.
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. Played almost straight with Brad Johnson, who was 41-years-old playing 42-year-old Rayford Steele. Dead-on with Kirk Cameron, who was 30 at the time playing Buck Williams, also 30 years of age.
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. This is a big part of the reason why the films are currently being rebooted.
The Other Darrin: In the first two movies, Bruce Barnes was played by Clarence Gilyard, Jr., before being replaced by Arnold Pinnock.
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, and was very happy when Gilyard did not reprise the role.
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.