Goofs

When walking back to his car after the first murder (0:30:39), Lou is carrying only his hat. When the camera angle changes to show him from behind, he suddenly has a wooden plank in his hand for no apparent reason.

Early in the movie, when Elmer Conway comes to Lou's house, Elmer's cigarette changes size repeatedly.

When Lou finds Joyce's handgun she says she "has a permit" for it. Texas has never required permits to own a gun, and until 1995 did not require permits to carry a concealed handgun.

Not requiring a permit does not mean she isn't allowed to have a permit. Texas still issues permits for those who want one.

Although possible in theory, it would be very unlikely that a small town Oklahoma sheriff in the 1940s would own an Italian Moka espresso machine, which had only just been invented in the late 30s and had real commercial success in the 1950s.

The movie is not set in the 40s. Judging only by the cars, it was set after ~1957. The newest cars (not counting anachronistic trucks) are 1958 models. Half of the cars are mid-to-late 50s models. His coffee machine is legit.

In the chase scene where Lou is chasing the bum through the streets to the town square, they pass a tanker truck with a modern cab.

When Lou Ford chases the extortionist down the street, the extortionist runs past a modern Peterbilt truck.

The gun that Lou kills Elmer with and then puts into Joyce's hand was manufactured by a company called Lorcin Engineering that operated between the years of 1989 and 1999, and therefore could not have existed during the time-frame in which the movie was set.