Actor Allusion: Will Ferrell's character breaks one leg, then later breaks the other. Mustafa, who Will played in Austin Powers 2, had the same misfortune.
A (sadly deleted) scene, fortunately on the DVD, features Max and Leo singing a duet that turns into a trio when a random stranger joins in. The actor playing said stranger is Ernie Sabella, which means that Timon, Pumbaa, and Simba were briefly reunited for a song.
Creator Backlash: The subject of sort of a meta-example (in addition to the obvious in-universe example). In season 4 of Curb Your Enthusiasm, Mel casts Larry David as Max on Broadway, knowing he's a terrible actor, in the hopes that The Producers will finally die because he's sick of it (see?). The season finale covers the debut performance with Larry in the role, and he starts to falter but manages to turn it around, ensuring the show's continued longevity.
Dawson Casting: Lorenzo St. DuBois seems to be a 50 year old hippie, not recent college graduate. (Of course, that could be the point.)
The original film was so offbeat and provocative it almost didn't get released - until Peter Sellers saw an early cut at a private gathering and pressured Avco-Embassy to support it, taking out an ad in Variety. (Ironically, Brooks had initially wanted Sellers for a role in the film but he turned it down.)
In a looser sense, this is the entire plot of the film—Bialystock and Bloom are meddling with their product, albeit to make it fail rather than succeed.
Fake Nationality: Franz Liebkind and Ulla; even though Uma Thurman has distant Swedish ancestry, she makes Ulla sound about as Swedish as, well, Hitler.
The Cameo: Mel Brooks provides the voices of the screeching cat Max throws, and dubbed the Stormtrooper who sings "Don't be stupid, be a shmartie, come on join the Nazi Party!"
Six Degrees Of Kevin Bacon: An example which does a complete 360: the movie and play was written by Mel Brooks, creator of "Get Smart," which starred Don Adams, who would later voice "Inspector Gadget," which would later be adapted into a movie with Matthew Broderick, who plays Leo in the play and 2005 remake of this movie.
According to Mel Brooks, he only let Hoffman audition for The Graduate because Brooks' wife, Anne Bancroft, was playing Mrs. Robinson in that film. Also, since Benjamin was a blond jock in the book, Brooks thought he'd never get the role.
Peter Sellers was the original choice Mel Brooks had for Leo Bloom.
Brooks originally conceived the film as a non-musical play, but realized it required too many set changes. He then played with the idea of it as a book, but it had too much dialogue. Eventually, he realized it could only work as a movie.