WIth a google search of "what city officials regulate the care of animals in pet shops?" the first thing that came up was this site...for Illinois, but it's highly likely that each state has the same thing, or something similar.
http://www.agr.state.il.us/AnimalHW/awflaws.html
Particularly this part of that site:
"The Animal Welfare Act provides for inspection and licensure of facilities that produce or offer certain animals for sale or adoption. Inspections ensure compliance with sanitation and animal health requirements. Several types of facilities are regulated under this act, including pet shops, dog dealers, breeding and boarding kennels, catteries, animal control facilities, animal shelters, foster homes, and guard dog services."
So then, after finding the particular phrase "animal welfare act" I googled "animal welfare california"
because I live in CA. I found the penal code for inadequate housing, feeding, heating, ventilation for animals sold in pet stores, but that did not give me the answer as to WHERE to report insufficient care of an animal in a pet store....which lead me to this from the ASPCA (nationally)
http://www.aspca.org/about-us/faq/pet-statistics.html
When visiting that site, if you click on "pet store complaints" you get this:
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Pet Store Complaints
I’d like to make a complaint about the conditions/treatment of animals in a pet store. What should I do?
In New York City
New York State is in the beginning stages of the pet dealer licensing and inspection process. In the meantime, if you suspect criminal acts of animal cruelty taking place, such as intentionally harming an animal or depriving an animal of food, water or medical care, please call 311. For other pet store complaints, please call the Department of Health at (212) 676-2115.
Outside of New York City
We urge those who do not live in New York to contact any or all of the following organizations:
Your local SPCA or humane society, which may have the power to investigate such matters in your area. For a listing of animal agencies in your area, visit ASPCA.org.
your local Health Department/Board of Health, as the abuse of animals in pet stores and breeder facilities often involves unsafe or unsanitary conditions for humans
your local Better Business Bureau
local law enforcement officials
local media organizations
local politicians
the U.S. Department of Agriculture, which oversees wholesale breeders of dogs and cats. It is best to contact this agency by mail.
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Long and short of it, I think the ASPCA is where anyone would start, for reporting a pet store in your own state/city nationwide. If nothing else, it looks as if they have the answers as to where to file a complaint about a pet store.
Honestly, I dont think you have much luck trying to tell a pet shop manager how to manage his shop. S/he might nod their head and agree, but even if they are sincere about agreeing with you, a chain store manager is going to look at costs - bottom line. And if it works, don't fix it. They have to answer to their corporate managers who probably really could care less because they are out of touch...and corporate managers are more motivated for overall profit than overall happiness of the animals.
Reporting them to authorities WILL get everyones attention, and Im sure you can do it anonymously so that you could potentially still shop there and go into the store to quietly investigate later if you choose to. And reporting them will cause the corporate manager to listen, because not only will it affect the profit but it also might result in a fine or the loss of license to continue selling the animals if they do not conform. But one person politely suggesting humane housing will most likely only get a head nod by the person who might have the title of only "shift assistant manager"...and then you would have to rely on that person taking the info to the shift manager, who would then have to take the information to the store manager and if it even gets that far, would then have to take it up with the regional manager...who might or might not care enough to take it up with the corporate management team. Unfortunately, and sadly, one person ...no matter how polite they are, will not get further than the assistant store manager nodding in agreement.