The reason Mia Farrow wears sunglasses most of the film is that Woody Allen did not feel she could pass herself as a tough Italian "broad", so he had her wear the sunglasses most of the film to hide her eyes, making her seem more sultry and mysterious. The only time she removes the sunglasses is when her character is supposed to be more vulnerable.
The movie makes mention of Weinstein's Majestic Bungalow Colony resort in the Catskills (Catskill Mountains). This is where Woody Allen got his start in show-business performing magic tricks there at sixteen years of age.
Dissatisfied with the original take of the scene, director Woody Allen re-shot the scene in which Danny Rose tries to sell acts to Phil Chomsky, re-casting comedian and singer David I. Kissel in the role of the owner of "Weinstein's Majestic Bungalow Colony". Kissel persistently called it "Mrs. Weinberg's Bungalow Colony" during filming, and Allen, exasperated, asked the actor why he kept saying this. Kissel explained that his wife always bought a brand of kosher chopped liver called "Mrs. Weinberg's Chopped Liver," and he kept thinking of that. Allen, amused, but ever the perfectionist, taped the words "Weinstein's Majestic Bungalow Colony" to the top of a filing cabinet in the office. As you view this scene, early in the film, you will notice that Dave Kissel faces away from the camera as he says those words, and speaks with his back to the camera: he is reading the words "Weinstein's Majestic Bungalow Colony" off that "crib sheet" on the filing cabinet.
In the film, it is touted that a sandwich be named after Danny Rose (Woody Allen). Its type and filling is suggested to be cream cheese on bagel with marinara sauce. In real life, after the movie was made and released, the Carnegie Delicatessen Restaurant, which was a setting in the picture, owner Leo Steiner, who appeared as himself in the film, created a "Danny Rose" sandwich. Its filling includes corned beef, pastrami and coleslaw and it comes in a special doggy bag. "Danny Rose" and comic strip character "Dagwood" are the only fictional icons that have a sandwich named after them at the Carnegie Deli.
During their relationship, Woody Allen loved to write roles for Mia Farrow that she had always wanted to play but couldn't because no one would believe her as this or that character. The character on this movie is a perfect example of that, because she wanted to play an Italian broad, and Allen was so sure of her talent that wrote it for her.
The deli owner who informs Danny Rose about the fate of one the characters in the movie was really the co-owner of the legendary Carnegie Deli where the scene was shot. He was a retired comic and actor who retained his SAG card named Leo Steiner. He was only cast after the actors Woody Allen brought to the location were inadequate.