After Mamie ties Emmett's necktie, it is not tucked under his collar in the back. Later in the same scene, it is perfectly tucked.
The TV screens, even though they have rounded corners and display black and white video in low quality, are obviously cleverly disguised modern LED screens: the picture is stable, there is no noise, no snow, no wavering sound.
The cover of Jet Magazine on Sept 15 1955 featured Beverly Weathersby on the cover and not Emmett Till and his mother with her fiance as depicted in the film. The article about Till's horrendous murder including photos was featured in the interior of the magazine.
In the scene when the men are getting haircuts in the barbershop. One barber is using a afro pick that wasn't invented until the sixties.
When Mamie walks past Polk's Barber Shop at 17:44, the front window advertises "unisex and nails". The term "unisex" wasn't coined until the 1960's.
The flashlights used by the sheriff and his deputy are LED, decades ahead of their invention.
In the beginning, after Emmett sings the Bosco chocolate syrup jingle he gives a High Five to Gene. However, the High Five wasn't part of African-American or American culture in the '50s.