Revealing mistake: During the opening musical number, after the baker says "Life's a piece of pie" and Gary is seen grabbing a plate with a piece of pie on it and tossing it over his head, watch closely. It becomes obvious that this is a fake piece of pie that is attached to the plate. Similarly, right before that, he grabs a cake out of another baker's hand and gives it to Walter, and you can see he is pressing his fingers into the "frosting", yet he leaves no marks, nor has any frosting residue on his fingers, revealing that was also a prop.
Continuity mistake: During the opening song, as Gary is dancing with the crowd, right before the chorus of the song kicks in, Gary spins around, with his hand to his nose like he's about to sneeze. During the first shot from the front, he puts his hand up to his nose, and begins to turn in a clockwise direction. He turns about 15° as the camera cuts to the next shot, and he has suddenly turned a complete 180° instantly between shots, and is facing the opposite direction.
Fozzie Bear: Wow, that was such an expensive looking explosion! I can't believe we had that in the budget.
Trivia: Frank Oz, the former voice of Miss Piggy and Fozzie, chose not to be a part of the film, after being dissatisfied with early drafts of the script. He later stated that he enjoyed the finished film for the most part, and that it didn't contain elements he had earlier objected to. (Though he commented that he didn't enjoy the "Disney Process" that went into the production of the film, and he felt that the film was slightly "too safe", though he enjoyed it overall).