Factual error: Midge talks about a 2 for 1 pantyhose sale but pantyhose weren't introduced until 1959.
Factual error: Taxicabs appearing in various scenes show that they are fitted with side marker lights on the fenders. Those were not used on American cars until 1968.
Factual error: In the Greenwich Village record shop, the vinyl records are shown with polythene sleeves. At that time, vinyl LP's were always factory sealed in cellophane shrink (unless it was later removed), not poly sleeves.
The Disappointment of the Dionne Quintuplets - S1-E4
Factual error: When Midge is moving to her parents' apartment there is a stack of books on the table while her son is watching TV. On top is a Nancy Drew book (the back of the book which is yellow). However publisher didn't introduce the editions with the yellow back covers until the 1960s.
Factual error: The word "floaties "was not used to refer to pool toys in the 1950's.
Factual error: When in Harrisburg, Susie mentions the Civil War Museum, but that didn't open until 2001.
Factual error: Abe hilariously exercises in a ridiculous suit while listening to Robert Preston's "Chicken Fat" recording. But Preston (who starred in The Music Man) didn't release this until 1962, at the behest of President Kennedy, who was big on physical fitness.
Suggested correction: It's true that this song was not recorded and released until 1962, which is a little after when this scene takes place. However, Abe is not actually "listening" to it (or any other music) while he is exercising on the lake dock. The song is used as part of the series soundtrack and creates a desired mood for the scene. As the storyline is now in the early 1960s, it is appropriate to the era, and is only background music.
Ethan... Esther... Chaim - S4-E7
Factual error: When Midge and Rose leave the club after the magicians act you can see tactile paving at the crossing. This can't be possible as tactile paving was first developed in Japan by Seiichi Miyake in 1965, so they're 3 years too early.