When Dane replaces the bloody sofa, his wife says she doesn't like the pattern because she wanted a floral print. We then see them both in a furniture store trying out a floral-print sofa. But later in the movie we see them both sitting on the "ugly" one she didn't like, and in a scene after that, they're on the floral print one.
Outside the restaurant, Ann shifts the car into reverse twice.
Jim Bob mentions the (Texas) DMV. There was no DMV in Texas when the movie was set. In 1989 those functions were handled by the Texas Department of Transportation. The Texas DMV came into existence in 2009.
The Red Btch car is involved in an accident with the blue Pinto on its back right corner. After Ben watches the video and gets in the car with a gun, one camera shot reveals no damage to the car at all. In fact the corner of the car appears to be purposely hidden prior to the no damage reveal.
When Jim Bob shows his private investigator ID, there is no photo, and it bears no resemblance to a Texas private investigator ID, which includes a photo (and did in 1989).
When Dane arrives at his store, a school-age boy on a bicycle is throwing newspapers. As Dane enters the store his wife calls him from school and tells him that students have been asking about the incident. The newspaper boy should have been in school.
Two 1989 Texas license plates shown, BEQ 9C5 and HJQ 3F2, were part of a numbering series not in use in 1989.
When Ben is reloading his pistol outside Jim Bob's place, we hear the cylinder latch shut three separate times before he shoots again. This makes no sense, as he would have loaded six rounds and then closed the cylinder.
There is a CSX train. CSX operates on the east coast, where the movie was filmed, but has never operated in Texas, where the movie is set.
Russell says he hasn't seen his son (25-30) since he was the same age as Dane's son (5 or 6). He then agrees to go to the cemetery to identify him! How would he know what he would look like?