Corabeth tells Jim-Bob that she can not sell him more than 3 dollars of gas due to rationing. This story takes place before December 7, 1941. The US government did not enforce rationing until after that date.
The song, Moonshiner, the Jason and Yancy sing at the still, wasn't written until 1961, so is out of place in this time period.
When Yancy and Jim-Bob show John their 120-proof alcohol, the shadow of a large film camera and a curly-haired camera operator's head is clearly visible, moving across John's shirt.