I really liked this story, in fact I'd rank it among my favorites, though there were plenty of things I didn't like about it. The "This is the same dog" repitition rang very nicely to my ears, and I enjoyed the trickster stories much more than I did the main narrative. I was looking forward to the next story as I was listening to the rest.
As others have said, I didn't much care for the master/slave imposition on the human/animal relationship. Most dogs these days are pets, though some do of course carry useful employment such as seeing-eye dogs, hunting dogs, drug-sniffing dogs. Even those working dogs have a mental disposition that it's not slavery, they are rewarded with treats and/or affection in a way that is very fulfilling to them. Yes, the existence of dogs was created by mankind's bending of the animals to their own wills over the course of millennia, but that does not make my dog a slave or myself a slave owner. Domesticated dogs existed before I was born. Furthermore, my three dogs are rescue dogs, which would have been killed if someone had not taken them in.
Another way that the story didn't mesh well is that everybody's relationships with their dogs became so antagonistic. Spoken language or no, once you get to know a dog it's not very difficult to read their emotions in their body language, whether they're happy, angry, sad, scared, sick, etc... So if my dogs were able to speak, it would be along the same lines of expressing the same emotions they've already expressed. And would probably be much more along the lines of that beer commercial where there is an obscure brand of beer that supposedly lets you understand animals, and the dog is just sitting there and yelling "Sausages" over and over again. The pooches are smart, but yeah sometimes they have a one track mind.
I didn't believe that the police could get away with poisoning a park full of dogs without anyone protesting it.
And where was PETA in all of this? Some PETA supporters already get very militant about animals rights the way it is now, don't you think that would magnify if the animals could speak for themselves? Even non-PETA groups might argue for animal rights if it could be argued that the critters are sentient.
And much more interesting than the dog relationship is the livestock relationship, which I was disappointed that the story didn't explore at all. The story even mentioned hamburger, so presumably they're still butchering the cows who can now talk to them. Me, I don't think I'll ever give up meat, but if cows started talking, I would go vegetarian immediately. It seemed like the author just wanted to stick to the dogs, but then it would've made more sense to just make the dogs alone able to talk. Ignoring the consequences of the rest of the domesticated animals just made the world seem more like a thought exercise, an allegory, than any place that could exist even within its own rules. I still really enjoyed the trickster tales, but that made it hard to get into the main part of the story.