Factual error: The film takes place in the Thirties. The song "You are My Sunshine" is featured, but was not recorded by Jimmie Davis (its composer) until 1940. [Acknowledged by the directors]. (00:11:15)
Factual error: When the escapees are hiding in the movie theater, the door opens and a deputy steps in, silhouetted by the light behind him. The movie is set in the 1930's, but the shotgun the deputy is holding appears to be a 1960's model Remington pump. (01:05:40)
Factual error: When the "Little Wharvey Gals" are singing they show a shot of the crowd in which there is a man smoking a filtered cigarette. Cigarettes were not filtered until the late '40's.
Factual error: Boy says he nicked the census man but the film is set in 1937. Last census would have been 1930.
Factual error: Notice the Confederate flag in the KKK meeting at night. This takes place in the 30's and they didn't fly the Confederate flag until the 50's. Before then they flew the US flag.
Factual error: Newspaper says "July 18, 1937" but Baby face died in 1934.
Factual error: Near the end of the movie, when the Tennessee Valley Authority flooded the valley after the dam had been completed, it is filled with water in a matter of minutes. In reality, it took months before the valley was filled to capacity.
Answer: Probably they have dismantled the coffer dam that was used while constructing the main dam. Hence, the flooding.
Good and reasonable last resort explanation - have the Coens ever addressed it?