Interesting. I had read that Brando said he stuffed his cheeks because he like the effect on his voice.
According to Mario Puzo, the character of Johnny Fontane was NOT based on Frank Sinatra. However, everyone assumed that it was, and Sinatra was furious; when he met Puzo at a restaurant he screamed vulgar terms and threats at Puzo. Sinatra was also vehemently opposed to the film. Due to this backlash, Fontane's role in the film was scaled down to a couple of scenes.
George Lucas put together the "Mattress Sequence" (the montage of crime scene photos and headlines about the war between the five families) as a favor to Francis Ford Coppola for helping him fund American Graffiti (1973). He asked not to be credited.
James Caan originally heard the phrase "bada-bing!" from his acquaintance, the real-life mobster Carmine Persico, and improvised its use in the film.