I am considering adopting a dog from a locally owned pet store, it a registered breed and has a pedigree. Is there any way I can check to find out if the dog is from a puppy mill?
The best way would be to visit the breeders, see the conditions that the dogs are kept in, and meet the parents. If the place seems clean and the adult dogs are sociable and have had some basic training, it's not a puppy mill.
If the breeder is too far away to visit, references from other breeders and puppy buyers are very useful. I'd also check out the breeder on Facebook, both the kennel page and their personal profile if you can find it. A pure money-making operation might have birth and death announcements, show results, and photos of dogs in a fenced yard or in kennels. What would be missing is evidence that the dogs are part of the family and regularly spend time interacting with people.
Unfortunately the answer is No, you can't. @kaynetoad mentioned the correct way if you actually know the breeder.
The reason you can't find it out is that dogs have different personalities and also physics. Some of their characteristics is purely inherited from their past generations. In plain English, you can't say If the puppy does A or looks like B, then it comes from a Puppy Mill, otherwise from a good and responsible breeder.
The only thing that you might consider when getting a puppy from a pet store is to avoid getting a puppy who's less than 8 weeks old. If you're selling a puppy in less than 8 weeks you're damaging the overall health of the puppy. If you don't care, probably you're not a registered Kennel -- so officials don't check what you do there, and you just wanna make a dollar out there.
Also based on paws.org:
Roughly 90 percent of puppies in pet stores come from puppy mills.
So, if you live in states and you don't wanna contribute to the Puppy Mills' businesses, then try to find a good breeder who is registered in Kennel Club. You can probably get a list of registered kennel's in your neighborhood if you simply ask them to provide it for you, I guess.