Mastroianni had a cute film-biz anecdote about this movie, noting that while promoting it in Manhattan he was having dinner at a posh Italian restaurant and the waiter, shaving a truffle over his pasta, motioned to Mastroianni whether he should continue and Marcello nodded yes, repeating "Paramount, Paramount" (the company was picking up the check).
Marcello Mastroianni grew a mustache for the film, but was so nervous on the first day of shooting that he absent-mindedly shaved it off.
When Antonio (Mastroianni) and Robert Traven (Lemmon) enter the home of Maria and her husband, the camera pans to a shot of three portrait photographs on the dining room sideboard: 1. a photo of Jack Lemmon in army uniform; 2. a photo of Pope John XXIII; 3. and ....... a photo of Enrico Berlinguer, head of the Italian Communist Party from 1972 to 1984. Maria's husband points to the photos and says: "These are our patron saints."
Jack Lemmon was an accomplished jazz piano player as demonstrated in this film. He also plays a jazzed-up version of "Silent Night" in Robert Altman's The Player (1992) during an outdoor party scene.