All of the Wonder Wheel cars that the characters are in, and the ones behind them, are all white. The long shot if the Wonder Wheel shows all cars are different, bright colors.
When Midge's family is at Coney Island, they make multiple references to playing Whac-A-Mole. However, Whac-A-Mole was not invented until 1975 (in Japan), and was not widely seen in U.S. carnivals and arcades until the late 1970s.
In her stand-up, Midge refers to klezmer music. The type of Jewish dance music was not referred to as klezmer until the mid-1970s, when the music was revived. Up until then, it was just referred to as "playing the freylekhs".
Midge uses the phrase "shit happens" in her stand-up routine in 1960. This phrase was first observed in 1964 and first seen in print in 1983.
Moishe tells Michael a Whac-A-Mole story while they're at Coney Island for Ethan's birthday. The series happens in the late 1950's. Whac-A-Mole wasn't developed until the 1970's, more than a decade later.
While visiting Coney Island, Abe refers to the midway game Whac-A-Mole which didn't appear in carnivals and amusement parks until 1980.