When Karl is talking to the Frostee Cream Boy, there are no cars on the road behind him. But whenever the camera is aimed at the Frostee Cream, there is a lot of traffic on the road reflected in the window. Billy Bob Thornton points out in the DVD commentary that this is because the local police had another pressing issue the day they filmed Jim Jarmusch, and they couldn't be there to stop traffic.
The morning after Karl slept at the warden's house the scene opens with an exterior view of a one-story house. The next shot is in the interior and shows a set of stairs that are obviously going up to a second floor.
When Jerry and Karl walk up to Bill Cox's repair shop for the first time, the Steadicam operator's reflection can easily be seen in the right front hubcap of Jerry's car. He is visible during the entire shot, which lasts about 10 seconds.
When Doyle drives to the county line to get more alcohol, they're in a "crew cab dually pickup", yet Doyle, Karl, and Vaughan ride in the front seats, the rest of the crew rides in the bed, and no-one rides in the back seats.
When Karl is killing Doyle Hargraves, there is a mirror visible in the background, to his left. You can see that Billy Bob is really hitting a table with a blue pillow on it, instead of Dwight Yoakam's head.