Ethan is watching The Howdy Doody Show (1947) in the evening. It's unlikely that this kiddie show was shown during prime time in New York in the late 1950s.
Midge comes home and her parents yell at her telling her it's 2 o'clock in the morning. She then proceeds to sit on the fire escape and watches a neighbors TV showing The Jack Paar Show, but that show always ended at 1 am Eastern time.
'Mark Twain presenting at Royal Albert Hall, 1904' is not a real album, and there is no existing recording of Mark Twain.
The term "Nerd" is used, and though it was a nascent term in 1958, it did not come to have its modern meaning, which is how it was used in the episode, until after early 1970.
At the rally, Midge mentioned a two for one sale on pantyhose. Pantyhose weren't used until the late 1960's when the miniskirt became popular. In 1958 women still wore stockings with garters.
The intended route of the Lower Manhattan Expressway was never through Washington Square Park. The park and the surrounding neighborhood is too far north.