It has been established in previous episodes that Dean is allergic to cats, and does not like dogs (especially in the episode Man's Best Friend with Benefits (2013) ). Ironically, in this episode he starts feeling like a dog, and even sympathizes with them, and stands up for their rights.
In the Taxidermy shop there is a mounted bald eagle. This is actually illegal to do in all 50 states.
While interviewing the dogs at animal control, several of the dogs make reference to famous prison movies, including The Green Mile (1999) and The Shawshank Redemption (1994).
The agent's rock aliases for this episode are Michaels and Deville. Bret Michaels and C.C. DeVille were in the band Poison. This could also allude to the fact that the brothers were meant to be vessels for Michael, the archangel, and the Devil, Lucifer, in earlier seasons.
When Sam says the restaurant is in violation of penal code 8.14, he is referring to the laws regarding domesticated dogs and other animals.