Your city should have enforcement rules that require him to maintain his property in a manner that prevents damage to your property.If the city doesn't help, then you can try paying for it yourself and sending him the bill.

On Airbnb I create a new account for them (or update theirs if they already have one) and add myself as a cohost giving my primary Airbnb account access and preventing multiple logins.

Are there any rules preventing me from asking about their pet?

The best part about Reno / Tahoe Nevada are it's landlord friendly, Real estate taxes don’t reassess on the sale, insurance is low and we continue to have increased in migration, jobs (no state income tax) and our own land constraint issues which prevent the market from getting overbuilt. 

Onsite weekly visits to open the faucets and expel the gasses, adding the necessary chemicals to my drains to prevent oxidation, handle the bills, proper property maintenance.

She should have been using rinse aid for the dishwasher to prevent Water spots or a better brand dish washer detergent.You need to nip all this in the bud.When my tenants ask for an upgrade I ask how much extra rent is this worth to you?

To focus on having less of bills for a potential loss of income is like getting a set of denture made just in case ones teeth rot out, vs brushing them (skills maintenance) to prevent the loss in the first place.  

Now, let's tackle it like a pro: Identify the moisture source causing the mold, fix it to prevent a comeback.

The reason for this is that you end up taking a short-term rental to pull in a few bucks and that ends up preventing someone that would have wanted the place longer.

If this was me, I would be at the property, getting in touch with local Facebook groups and generating bids to get handymen/local contractors taking up urgent jobs that are preventing units from being rented (even at a lower premium) that are ready to help nurse the deal.