No sooner had we even closed on the property than they found a tenant ready to move in.

I imagine those renters will fill it and then not access it much, so it shouldn't be a bother to your tenants.

Prices are high, regulations favor tenants, and finding deals that truly pencil out can feel like looking for a needle in a haystack.

We run into this especially at out parcels in grocery anchored centers, and our users generally can't make a ground lease work for the business case so the next best thing does tend to be the BTS or we often do Reverse BTS deals where the majority of the building design and management etc is done by the tenant. 

Why is your tenant paying you by credit card? 

Tenants were unwilling to pay the higher rent for units which included heat and hot water. 

For example: If a tenant applies for a $1,000/month rental and they have gross monthly income of $3,500 they meet the first criteria, but when applying the second criteria you find they have a $500 car payment and $250 child support payment.

Not one single example, yet everyone pushes it like it's the ultimate protection policy.As stated above, the best protection is to follow the law, treat your tenants honestly, and document everything. 

I have a tenant in my Rosewood rental who is saying that the water in the shower is coming out cold even after she lets it run for a bit.

Did you find any prior knowledge (tenant screening) of pets moving in?