The story takes place in 1964. Throughout the story, June wears a silk-screen NAACP t-shirt. Silk-screened t-shirts did not exist until the issuance of a patent for the garment screen printing machine in 1969.
The action in the movie took place in July, 1964. When we first meet Zach, he is singing The Four Tops' "Baby, I Need Your Loving," which was not released until August 15, 1964. A few scenes later, the characters are listening to The Supremes' "Come See About Me," which was not released until November, 1964.
When Lily and Rosaleen are drinking their Cokes on the grass outside the Boatwright house, you see Rosaleen drink the last of the soda, but you can clearly hear the liquid flowing back into the bottle.