During an interview before the race, Seth MacFarlane's character says his driver and race team will be drinking his energy drink after "lap 600". The Coca Cola 600 is 600 miles, not 600 laps. This is also confirmed later when an on screen graphic shows the current lap "of 400". This could be intentional to indicate that the character is not interested in racing, knows very little about it, and is only interested in advertising his product.
Mellie crosses into North Carolina at Surry County, which makes sense when traveling from West Virginia, but Charlotte Motor Speedway would still be over 100 miles away to the south, not the short sprint suggested by the film.
Every Lowe's employee knows you are not allowed to take your red vest out of the store. The only time you can do so is if you are working on some kind of community project with a team from the store.
Jimmy Logan is depicted as commuting to his job at Charlotte Motor Speedway from West Virginia. By the quickest route, straight up I-77, the WV border is 2.5 hours away.
This is also a problem for the heist, which supposedly takes place over the span of a couple of hours. There is no way everyone involved could have driven to Concord, NC, where the speedway is, pulled the heist, and returned to wherever in WV they were, without being gone for at least most of a day.
The Coca-Cola 600 is depicted as taking place in broad daylight. The start of the time of the race is usually a little after 6 pm, which is sunset local time, and it's dark not long into the race.
Several characters refer to Interstate highways (such as I-17 and I-19) which do not run through West Virginia. (They might have been referring to US routes, but US 17 does not pass through West Virginia.)
The first wide of shot of Charlotte Motor Speedway shows mountains in the background. Charlotte Motor Speedway is nowhere near mountains.
Jimmy is depicted as driving from Charlotte Motor Speedway to West Virginia. He crosses the WV border on a relatively flat country road. North Carolina does not border WV; any route would necessarily take him through Virginia. The border of VA and WV is very mountainous, and on his most reasonable route, along I-77, the border is at a tunnel going though East River Mountain.
Mellie gives directions from Jimmy's work at Charlotte Motor Speedway to Charleston, WV, but they make no sense. The only reasonable route is to take I-485 from Concord, jog over to I-77, and follow that all the way to Charleston. It would be a trip of more than 4 hours.
The F150 was an F100 earlier in the movie.
Outside of Southern California, most Americans don't refer to interstates or numbered highways with "the" as a prefix. Mellie refers to an interstate as "the 19," something unlikely for West Virginians.
Moody attempts to get Mellie to trade in her Chevrolet Nova for a brand-new Ford Mustang V6. At the time of the film's release, Ford discontinued the V6 model, as it was outsold by the EcoBoost 4-cylinder model.
When Joe puts the explosive bag into the cash container, the top of the bag is caught in the lid. The container is is fired through the tube with the lid at the back. The container is then fired back and into Clyde's chest with the lid facing away from Clyde. This wouldn't have happened as the lid was last in it should have been first back out of the tube.
When Max Chilblain is in the bar ordering a second Stoli, he says: "I want to shoot a post". He clearly says something different, and the word "post" is dubbed.
When we are introduced to Clyde he is tending bar and Jimmy goes there after being "let go" from his job. Toward the end of the scene, Clyde picks up Jimmy's empty glass, but then in the next shot the top of the glass can be seen sitting on the bar where Jimmy had been.
In the rural mobile health clinic scene, the medical provider is a Physician Assistant, NOT a Physician's Assistant. PAs are medical professionals and health care providers, they are not property or owned by the physician.