The basic premise of this film is that Gonzo is an extraterrestrial alien. 20 years earlier, in a "Veterinarian's Hospital" sketch on The Muppet Show: Raquel Welch (1978), Rowlf suggested that Gonzo should "leave his body to science fiction".
The voice of Baab the Sheep was eleven year old Kristina Donnelly, who was given the opportunity through the Make-a-Wish Foundation. Kristina wanted to be an actress in a Muppet film, but when given a choice between that and voicing a puppet of her own (the suggestion made to her by Steve Whitmire and Dave Goelz), she chose the puppet. Near the end of her time filming Steve and Dave presented her with a special edition of the Hensonville News Observer and a bag full of Muppet merchandise. The puppet she voiced, Baab, was also given to her.
The last Muppet movie to have Frank Oz's involvement. For most of production, Frank Oz was not available so substitute puppeteers performed his characters, and Oz later dubbed the voices during post-production.
The original concept was based upon the song "I'm Going to Go Back There Someday" which Gonzo sings in The Muppet Movie (1979). Muppeteer Dave Goelz recorded a new version of the song (in 4/4 time) but it was not used in the film. It was included on the soundtrack album, however.
The first Muppet film since the deaths of Jim Henson and Richard Hunt to have their signature Muppet characters (Rowlf, Scooter, and Dr. Teeth) talk. Rowlf's only line is "Awwww!" at the breakfast table, when he finds out they're having bologna. Dr. Teeth's only line is "Shalom!", on the way to a bar mitzvah. Scooter was voiced by Richard's brother Adam Hunt, and his line is "Get your Gonzo T-shirts. Only ten bucks!"
The band Ween was asked to provide a song for this movie. It was to be for the scene in which Gonzo was sitting on the roof dreaming of where he might have come from. After the song was recorded, it was decided that all of the music in the movie should be funk/soul and they asked Ween to record a remake of "Brick House". They declined.
The trivia item below may give away important plot points.
Originally the idea for the film was that aliens had seen Gonzo on The Muppet Show (1976) and came to visit him on Earth. Gonzo would believe he was one of them until he discovered the truth at the movie's conclusion.