The Wedding of Bobby Hill - S3-E14
Revealing mistake: During Rad's haircut from Luanne, there is a shot that shows the both of them in the mirror. You can see both their reflections and the room in the mirror but the objects on the counter in front of Rad have no reflection.
Revealing mistake: Whilst Bobby is reversing the truck before hitting the flagpole in Bill's yard we see the driveway in front of the truck. The very next shot shows Peggy from behind the truck instructing him how far to go to the flag pole and you can see they have used the same background as the shot before from the other angle. You can tell this as both shots are the same background as both angles despite from different viewpoints are exactly the same items and objects in both shots. Added to this there is a driveway in each shot, and Bill doesn't have 2 driveways in his backyard.
Born Again on the Fourth of July - S13-E14
Revealing mistake: When Bill throws a flare into the shed, the owner of the shed warns everyone about it containing all his fireworks. For 2 seconds the man's arm is coming out of his chest. (00:20:30)
Answer: Jeffrey Boomhauer is a Texas Ranger as can be seen in the final episode at the end when he sets his wallet down, it flips open revealing a Texas Ranger badge.