Statler and Waldorf popping up at random points in the movie.
A slightly longer version of the Kermit-Fozzie dance number in the El Sleazo Cafe.
An extended version of Doc Hopper's commercial.
An extra verse in both "Movin' Right Along" and "I Hope That Something Better Comes Along", both of which appear on the soundtrack album.
A more in-depth version of the reading of the screenplay (including a reference to "a large yellow bird").
A longer conversation between Doc Hopper and Max before they encountered the rainbow-colored Studebaker.
Gonzo's reasons for hitting Fozzie's Studebaker were originally different. Doc Hopper, while eating breakfast in the back of his limousine, accidentally sprayed a bottle of maple syrup onto his clothes. He attempted to clean the mess up with some tissues, but those ultimately got stuck to his suit. Eventually, tissue-covered Doc somewhat resembled a giant chicken, which distracted Gonzo.
Kermit and Piggy on a Hawaiian honeymoon during the "Never Before, Never Again" montage.
Sam the Eagle appearing on a sign that reads "Keep America Clean."
In Memoriam: The movie is "dedicated to the memory and magic of Edgar Bergen", who'd died shortly after filming his cameo appearance in 1978, and who was a major influence on Jim's early work. He and his puppets also appeared as The Muppet Show guest stars prior to this film.
Reality Subtext: Edgar Bergen and Charlie McCarthy made their last appearance in the film — Henson was inspired to make the Muppets because of him. Bergen died not long after his scene was shot, and the film is dedicated to him.
Talking to Himself: One of the benefits of this and the other feature films was the opportunity it afforded for characters like Jim Henson's Kermit and Rowlf, Frank Oz's Piggy and Fozzie, etc., to interact in a way that wasn't always technically feasible on television.
Despite the phenomenal success of The Muppet Show, it was not easy to get financing for a movie that was to feature puppet characters as the leads, especially in a decade when most A-list films were aimed strictly at adult audiences, leaving Disney and independent outfits to pick up the slack of films appropriate for children/families with modest-to-low-budget, mostly critically-disregarded productions. In the end U.K. company ITC Entertainment, which backed The Muppet Show in the first place, bankrolled the film, which was released through Associated Film Distribution, which was formed to release ITC and EMI's movies State-side (see Creator Killer for what happened to them).
Some of the bigger setpieces, such as Gonzo's Balloonacy flight, were not easy to pull off.
Director James Frawley had no prior Muppet experience; Henson and co. hired him because he did have feature film experience and they were new to that particular medium, but it did mean that he was an outsider to the tight-knit group and this led to on-set disagreements and tension. Austin Pendleton, who as Max was one of only two actors around for a significant chunk of the shoot (the other being Charles Durning as Doc Hopper), didn't find it a happy experience as a result (save for working with Durning, a case of Mean Character, Nice Actor).
One of the biggest one to note is the recurring appearance of Henry Kissinger, whose entire schtick is that he's not cast in the movie, not even for the Framing Device. Hilarious in Hindsight again?
Jim Henson wanted Doc Hopper to have a Heel–Face Turn at the end, but Frank Oz disagreed, and won out.
Max was initially a minor character. Austin Pendleton was offered the role, but initially turned it down, feeling the part was too small. The Max character was rewritten, and about a week later, Director James Frawley convinced Pendleton to appear in the movie.
"Never Before, Never Again" was originally supposed to have been sung by Johnny Mathis. After Mathis recorded the song, Jim Henson figured it would be much funnier if Miss Piggy sang it. But Mathis' version of the song wouldn't go to waste — it was featured in the television special The Muppets Go Hollywood.