Sylvester Stallone appears uncredited as a subway thug. This was one of his earliest film roles, not a cameo. According to website Every Woody Allen Movie, "Allen initially sent Stallone back to the casting agency after deciding he wasn't 'tough-looking' enough. Stallone pleaded with him and eventually convinced him to change his mind".
According to the Eric Lax biography, the musicians in the dinner scene at General Vargas' house were actually to be playing instruments, but the rented instruments hadn't arrived, and rather than wait, Woody Allen decided the miming would fit with the tone of the film.
The movie's mock-TV ad for New Testament cigarettes earned the movie a "Condemned" rating by the Catholic Church.
During the trial J. Edgar Hoover testifies, disguised as a black woman. While it was meant here as a joke, it would be revealed to the world after he died that Hoover may have liked to wear women's clothes, something that no one at the time of the movie would have ever believed. The connection is most likely entirely coincidental, as the rumor of Hoover's cross-dressing wasn't widely known until the publication of a 1993 biography. There were much earlier rumors about other aspects of Hoover's sexuality, however.
The third feature film directed by Woody Allen, and the first in which he had nearly full creative control.