When Jack grows ill while Bertha washes his foot, and out of the church, he leaves a boot behind. He is seen limping through the woods wearing a single boot. When he arrives at Cricket's cabin and is beaten outside the cabin by Charlie Rakes, he is shown wearing two boots. In the next scene, back a the Bondurant's Inn, Forest gives Jack a bag (a "present" from the preacher, Bertha's father). In the bag is the boot he left at the church.
When Jack and Cricket are driving with the truck full of moonshine, the amount of crates in the back of the truck changes several times.
When Floyd Banner is introduced, he shoots down several men in a car in the center of town with a Thompson submachine gun. Near the end of the scene the rear of the car is shown with bullet holes in it, but Floyd Banner was never behind the car, and he could only have put holes in the side and front of the car.
When Floyd Banner hits Gummy Walsh with a shovel, Gummy lands with his legs stretched out straight. But the wide camera angle his legs are bent.
When Jack and Cricket run out of gas, Jack snatches off his hat in frustration at Cricket, in another camera view he snatches off the hat again.
Jack said that the Prohibition Act was passed in 1920. It was passed in 1919, and went into effect in 1920.
When Floyd Banner is arriving in his car and stopping to eliminate his competitor, you can hear the sound of tires screeching on pavement. However he's driving on a dirt road.
In the final battle, the cops are blocking the bridge, but when Jack is chasing down Charlie and you don't see the blockade of cars behind them.
You can see the ground give way when Jack Bondurant is thrown off of the porch by Charlie Rakes while being beaten.
The movie is set in the 1930s, at one point a character is loading a shotgun with plastic shotgun shells, but plastic shells weren't introduced until the 1960s. During the period of the movie shotgun shells were made of thick paper with a metal bottom for the primer.
The box camera that Jack took photos with throughout the last half of the movie was a Kodak Brownie Target Six-20 which wasn't in production until 1946 - nine years after he used it.
The double-yellow line on the paved road in the opening scene. There would hardly have been any pavement in rural Virginia, let alone stripes, at the time.
When Jack and Bertha are riding in the car several mail boxes are seen on the side of the road, several boxes have reflective house numbers on them. That was not available during that era.
Telephone (utility) poles shown in several scenes include both telephone lines and cable TV lines, some of which include modern "expansion loops." Cable television wasn't introduced in the US until 1948.
Maggie says, "Forrest come dance with me," but her mouth doesn't move.
Heavy kudzu growth is visible in many scenes - this is an invasive plant species introduced to the United States in the early 20th century, and it's much more common in Georgia where the film was shot, than Appalachian Virginia where the film was set. And it probably wouldn't have been in either of those areas at all in the 1930's.
The flowers at Cricket's funeral (ranunculus, wax flower, French anemones) would likely not have been available in the rural mountains of Virginia at the time. They would have likely used wildflowers such as goldenrod and queen anne's lace.
Throughout the movie, Spanish moss is shown. The movie was shot in Georgia, which has Spanish moss. Franklin County, VA does not.