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 film is based on the novel 'The Wettest County in the World' by Matt Bondurant. The story is based on Bondurant's grandfather and granduncle's exploits. Whether it's true or not is harder to say.
Q
What are the differences between the R-Rated Version and the International Uncensored Versions?
A
Lawless is one of the very few cases where an Uncensored Version has never been released in its country of origin. While the US releases only offer the Censored Version, the Uncensored Version is only available in foreign countries. All in all, 9 scenes with 9 seconds have been censored to get an R although it adds almost 9 seconds in an alternate scene and two further trivial short scenes. The motives for those alterations are unknown. Maybe the studio was trying to cover up the censoring by adding "superfluous" footage to reach the length of the Uncensored Version. A detailed comparison between both versions with pictures can be found here.