Most states the pet stores are regulated by the State Dept. of Agriculture. I know this sounds odd but any animal related business not involved directly with native species comes under agriculture. Go figure and the animals in question are "livestock" not unlike cows and sheep. There should be a certificate of some sort posted in plain site, usually near the checkout, of the authority that regulates any pet shop. If you don't see it ask them where it is, if they refuse to show it then they are also in violation for that. These are the people to contact as it is their inspectors that have the authority to handle all complaints. For expample in Illinois its the State Dept. of Agriculture, Animal Welfare Divsion. You want to ask to be put in contact with the inspector for your city and file your complaint directly with them, insist on it, don't just file by phone with the receptionist/secretary. If possible try to have a cup of coffee with the inpector and file a written complaint and be informative as to what to look for. These guys have a job to do but are grossly undereducated as to the specifics. Be helpful to them not argumentative or offensive. Be specific in your complaint, DON'T just say the cages are filthy. If they have mites specify, dirty cages, runny stools etc. For the best impact don't just complain about the condition of the herps. Check out the whole store, even if you have no interest in the other animals. Look for sick, underfed, debilitated animals, mites on rodents, tanks full of dead fish, empty food bowls, water bottles. The more thorough you are in your complaint the more impact it will have on the store. These inspectors are usually overworked and understaffed and without specifics they may and usually do miss, what we would consider obvious. In most cases the animals will be put into quarantine by the store in question and cannot be released for sale until there has been a follow up inspection to see that the matter has been resolved. In severe cases I have seen customers asked to leave the store and the store closed until problems have been solved.
In the case of the mites you mentioned be sure to go back to the store at a later time. It's easy for a pet shop to clean cages, use a product that simply eradicates the mites on the herps but not the mite infestation in the store. The mites are usually back with in a week or so. This is why it's best to meet with the inspector so you can explain about how mites can migrate and that the whole environment needs to be treated not just the herps in question. Educate don't offend.
The police, animal shelters(who are regulated by the same authorities as pet shops) have little that they can do in regards to these complaints.
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Hope this helps.
BigT