Though never spoken in the film the name of the town where it's set is Mercer, Montana according to the script. The local population of the fictional town is 1,536 - though it drops over the course of the film.
The film was titled "Il Sapore del sangue" for its release in Italy. The title translates to "The Taste of Blood", referring to the scene where Lester licks his finger after cutting it on a kitchen knife.
The shot starts off with a full sized powdered donut being dipped into a red coffee mug thats obviously too small for the huge donut. Next shot is Clay's boss bringing a half-eaten donut to his mouth as Clay walks into the shop, apparently late again. He looks over his shoulder, and back to the donut. He then brings a large white styrofoam coffee cup into frame and dips the last bit of donut into it.
The patch's on Sheriff Mooney's and his deputy's uniforms read "Mercer County Sheriff's Dept". But when Mooney is driving a sheriff's dept SUV, the decal on the door reads "Davis County Sheriff".