I love the Sopranos. Maybe it's partly 'cause I grew up in Central NJ and enjoy seeing many familiar locations (especially Down The Shore).
My greatest objection, the thing that seems most unrealistic and out-of-whack (pardon the pun) is the incredibly stupid name some writer chose, early on, for Tony's daughter. No Italian-American family, not matter how "assimilated," is ever going to name a baby girl "Meadow." If for no other reason, you have to use a saint's name to be baptized in the Roman Catholic Church, and the Sopranos are (quite realistically and characteristically) practicing Catholics, despite all the murder and mayhem.
Over the years, we've all gotten used to this character's name and it doesn't seem so grating as it did at first. But it was wrong from the git-go, and it's still wrong.