Rodeo Days - S4-E12
Continuity mistake: Near the beginning of the episode when the Hill's are having dinner, you can see Hank's glass in the first shot is to his left. Next shot it's to his right.
Rodeo Days - S4-E12
Deliberate mistake: When Bobby is trying out for the cattle roping at the rodeo, he gets the rope tightly around the calf's neck. As the calf starts to drag Bobby you can see the rope is now very loose around its neck. A little later when the clowns are chasing each other the rope is back tightly around the calf's neck. May be deliberate as it may look like the calf would have been choked with the rope being so tight around its neck.
Rodeo Days - S4-E12
Continuity mistake: Whilst Bobby is first talking to the rodeo clown, the guy in the red shirt has some red paint under his nose. When the angle changes and shows both clowns the red paint has disappeared.
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.