Stanley Milgram in the film states the origin of his last name is Hebrew for pomegranate. "Milgram," however, derives from the Yiddish word for pomegranate, not Hebrew.
(around 10 min) When our leads are conversing at the party you can see a 2010 or newer Amana refrigerator in the kitchen with the freezer on the bottom.
In the end credits, Ned Eisenberg is listed as playing "Washington" (one of the test subjects) as well as Solomon Asch. Washington is played by Frank Harts.
The Coca-Cola cans are from the late 60s into the 70s. Not from 1961, the time of the movie.
When Stanley Milgram talks to the man dressed as Abraham Lincoln, modern cars passing by can be seen in a window reflection. This scene is set in the 1970s.
In scenes set in 1961-1963, Stanley Milgram owns a 1966 Plymouth Belvedere.
John Leguizamo is smoking Camel filters, which didn't exist until 1970.