The Italian-American Community
Even though the filmmakers did their best to make sure the Italian-American community was well represented, many folks were displeased with the films. When they were filming on-location in New York, many locals took it upon themselves to relate their concerns to the filmmakers.
They Didn't Love It
The locals were afraid that these films would exaggerate pre-existing stereotypes that people have on Italian-Americans and the mob world. In order to keep things civil, they eventually brought on true Mafia members to work on the film to showcase that the stereotypes are just that: stereotypes.