Continuity mistake: During Ulla's audition, at some point she is behind the desk somewhat bending over Max. Her veil falls down on her left arm. There is then a cut and her veil is back up in its proper position, then in the next cut it's back down as it was two cuts before.
Trivia: In the first scene in Max's office, there is a calendar showing the date as June 16. Leopold Bloom is a character in James Joyce's Ulysses, which recounts the events of a single day. June 16th.
Trivia: Mel Brooks "composed" the music for the Broadway show (which would go on to become this movie) by humming tunes into a tape recorder. Someone who was musically literate would then write it down on staff paper.