When Abe Weissman enters his study to view the Bell Labs documents brought by his son, he is not wearing cuff links. But when he comes out excited that there are two cafeterias, he is wearing gold cuff links.
The Elektra record label shown at the end is from the late '60's (e.g., The Doors), nothing like the late '50's label.
In the cab on the way home from the Chinese restaurant, Penny Pan (Holly Curran) says "I wonder if there really was a General Tso", referring to a famous dish, General Tso's Chicken. This dish wasn't created until the 1970's at Peng's Restaurant in Manhattan.
In her comedy routine, Mrs. Maisel says "There he was, handcuffed, being perp walked into the station." Her 1950's audience would have had no idea what a perp walk was. The first reported use of the phrase was in 1970, and the first documented use was in 1986.
The song the men were singing at the bar was Tom Lehrer's "Send The Marines," which wasn't written until 1964.