The Boy Scouts (Kinsey and his friend) are wearing the World Crest emblem which did not exist in the late teens when this scene supposedly took place.
When young Kinsey argues with his father in the general store, the actor's prosthetic nose is extremely visible, several shades darker than his skin with wrinkly edges
The newspaper headlines about Kinsey's first book in the late 1940s are pasted onto current newspapers. Just above one of the headlines we see a story about the New York Mets and the Houston Astros. These teams did not exist in the late 1940s.
When Kinsey and his wife are in the woods in New England one afternoon, they hear a whippoorwill, but the whippoorwill is a nocturnal bird.
The credits wish to thank the "University of Indiana". The correct title of the school is "Indiana University", there is no University of Indiana.
Kinsey is talking with reporters upon arriving in New York and his dialogue does not match up with the shot of him.