Spike Lee was facing a lot of negative feedback from the family members of the victims who didn't want a film being made which might glorify the killer in some sorts. As a result, the script had to be changed which focused more on the community than the killer himself. "Son of Sam" was rumored to be the original working title.
In the script, Richie (Adrien Brody) was the lead character while Vinny was a secondary character. But Spike Lee enjoyed John Leguizamo's improvising so much that he ended up giving him more screen time. The scene where Vinny pours coffee on Gloria was one of many improvisations by Leguizamo.
The wall at the beach club which Vinny and the guys hang out at has an Italian flag painted on it. This flag was painted there by the filmmakers before shooting and remains there to this day. The community is actually more Irish/German than Italian.
In the beginning of the movie, Vinny and the gang go to a disco called Virgo. There is actually no nightclub there, but the outside was painted to make it look so. The Virgo sign remains painted on the same building to this day.