In the opening credits the camera pans the skyline of NY, and shows the construction of the Twin Towers in the background. The movie is set in the late 1950s and the Twin Towers were not constructed until the 1970s.
Shortly after leaving the jewelry store, some of the characters are standing in front of a shop with a magazine rack. Some of the magazine titles weren't available until the 1960s. The movie is set in the 1950s.
When Chico takes Jane to the drive-in, the license plate number of the stolen Packard changes. When they arrive at the theater it is SV-5875, yet when they start to pull out, the plate has changed to 4N-4290.
After Stanley buys the ring for Frannie, Stanley starts walking with his right arm over Frannie, and his left arm over Annie. In the very next shot, his right arm is over Annie, and his left arm is over Frannie.