This movie is set in 1956. However, we see the Staten Island Ferryboat "The Gov. Herbert H. Lehman", which didn't go into service until the mid-1960s.
During one shot, the Bayonne Bridge is shown with the Goethals Bridge beyond it, on the right. Adjacent to it, the B&O Arthur Kill Vertical Lift Bridge is shown. This wasn't built until 1959, replacing an older swing bridge.
When Mary was shopping for groceries to make dinner for Buddy, on the shelf was "Victoria Vodka Sauce". Vodka Sauce was not available in the 1950s.