Many of Hannah's scenes were filmed in Mia Farrow's apartment. Woody Allen said that Farrow once had the eerie experience of turning on the TV, finding a chance broadcast of the movie, and seeing her own apartment on TV while she was sitting in her apartment.
The character of Frederick, played by 'Max Von Sydow', complains bitterly while watching TV that if Jesus were to come back and see what religion had become, "he'd never stop throwing up." Von Sydow played Jesus earlier in his career in The Greatest Story Ever Told.
According to a 2014 podcast with the director, Jack Nicholson was the first choice for the role of Elliot and was interested in playing him, but would have conflicted with the schedule for Prizzi's Honor (1985).
The trivia item below may give away important plot points.
The doctor tells Mickey they'll never know what caused the hearing loss in his ear. Later in the film, during a flashback to his first date with Holly, Mickey complains that the loud music at a rock concert made him him lose hearing in one ear.