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.
Won't You Pimai Neighbor? - S4-E18
Deliberate mistake: Before Bobby takes the final spiritual test, you can see Connie is behind Bobby with her parents. When Bobby starts looking at the objects she has moved over to the right of Bobby nowhere near were her parents were before. This would have been deliberate for when he's taking the test he picks Connie in the mirror and this would have been impossible to do if she was right behind him.
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.