My concern is that someone is going to damage something and not take responsibility for it.

This is only going to get worse and cause more damage. 

A rotten flange can cause raw sewage to get into the basement, water damage and what not, but it should have zero effect on the water bill.

re: moisture damage. were the pipes sweating that much to cause such extensive damage or what is the alleged cause of "moisture" from the ductwork?

It's a smaller house so the premium for replacement cost over 10 years vs the actual cost of replacement in the event of serious damage might break even. 

The other part I didn't see mentioned is that you should charge the tenant 100% of this service cost for the repair assuming your lease makes mention of tenant caused damages being their responsibility.

Such as smoking or causing damage to the hotel room?

This is my old insurance hat coming out, but garage parking also opens the door to potential damage with mirrors clipping the side walls, issues with the garage door getting hit, etc. 

The tenants are a couple of young  brothers who I'm finding are treating the house as an apartment an do not realize they have some responsibility in maintaining the yard and reporting any leaks or damage. 

So he’s causing no damage to my property