GF was wildly popular among real Mafiosi. FBI and other law enforcement who were bugging mobsters picked up many conversations about the film--all of them admiring--and caught mob guys and wannabees talking like people in the film.
As you probably know, Joe Columbo muscled Paramount to delete references to "Mafia" and "Cosa Nostra." In return, he gave the crew lots of cooperation during filming. He also let James Caan follow around some of his gang to study their ways. Caan mimicked Carmine (the Snake) Persico, who was then a Columbo capo. The FBI, which didn't know Caan, for a time had him listed as a new Columbo "made guy."