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: 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: Boy says he nicked the census man but the film is set in 1937. Last census would have been 1930.
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?