My first thought was “scam”. Maybe they do things different in the USA, maybe some minor officials are way too self-important (I always thought that was more a european trait). But inspecting apartments at the request of landlords, without charging a significant fee, without grounds for a serious health or safety complaint, sounds very unlike your typical government office today.
BTW, impersonating an official is generally a “bad thing”. You could maybe lay trespassing charges, say you would not have invited the person in if you had not been told he was an official county inspector and you were obliged to let him in. Does your area have a landlord-tenant act or similar? They usually list what rights the owner has to enter a rental property. (if the county and police don’t go after him first)
Second - was the letter on official county letterhead? I would think if this is the normal course of events to have a regular inspection at the request of landlords, then the result would be an official form with checkboxes and a few boxes where comments for various items would be written - most likely during the inspection. Think how much extra work it is to compose a letter back at the office, especially if he was not writing notes at the time.(did he take notes on a clipboard?) How long was the inspection? Between travel, waiting for the landlord to meet up, inspection, and composing the letter the guy would be lucky to get 3 or 4 inspections a day done. This is hardly a good use of government time; especially doing it as a free service to landlords with no reasonable cause to inspect. I would complain to your city councillor or whoever runs the government that takes your taxes to pay this guy, if he is legit. In fact, I would raise holy hell. If this guy makes $40,000/yr he makes about $20/hr, the landlord is getting $40 to $60 of free service for no discernable value to the county.
If he’s doing an assessment of the home, did he check for hot water, check the fuse box, or anything else that would be included in a “fit for habitation” inspection? Did he check the smoke detectors to see if they worked? If all he did was concentrate on cleanliness, then I agree the major mention should have been the cat feces.
(An elderly relative had a few dogs and cats, and even the hardwood - especially the hardwood - was ruined beyond repair because she indulged several animals too old to contain themselves for a decade. Even hardwood can be wrecked.)
If the letter did not mention the ordinances that were being violated, did not have official county letterhead, did not come in a county envelope, I strongly suspect scam.