This episode reminds me a lot of the tenth season episode "Portrait of the Artist as a Young Clown." The storyline is just weak, and seems more like B-story material - it can't quite carry the episode alone.
One of the things that bothered me the most was everyone's willingness to go along with the diversity instructor's wacky idea. I love that King of the Hill is presented in such a way that it could be happening in real life somewhere in Texas, but this plot is too extreme to have everyone in a normal society going along with it. While Lucky running from medical attention for his wire-barbed hand was funny, it was more slapstick and outlandish than most storylines, straying from the underlying context of reality King of the Hill.
While the whole thing involving Lucky and the barbed wire frisbee was a little slapstick-y for my taste, it did have some funny moments, particularly when he had slathered himself in Vaseline and the guys couldn't hold onto him. Re-watching the episode,I thought it was funnier the second time around, however, the other elements of the episode did not improve with a second viewing.
This episode wasn't awful, but it was a little disappointing, especially following twelfth season gems like "Death Pickks Cotton" and "Raise the Steaks" (although Hank raising cows in his backyard isn't exactly the most realistic element to hit the show). Overall, it was slightly forgettable but did make me look forward to better episodes this season.