I have a pet-friendly home that currently has a tenant that has been residing in it for a month and a half (she does not have any pets) and is complaining that her allergies and asthma are being affected.

Write off anyone who has young kids or pets who could drown unless you have a legit pool fence around it and even then... liability.As much as I LOVE pools, I think the liability and maintenance costs outweigh the marketability of a home with a pool for an investment scenario. 

BackgroundThey left behind a lot of pet damage, completely destroyed the grass, tons of missing items and didn't clean much before they left.

The duplex is a fairly nice 3b/3ba within walk/bike distance to Bay Area Rapid Transit (BART) with tenants on a month to month lease at pretty much market rate (also they have pets if that means anything at all re: stability). 

I allow pets in my rentals, however make sure you charge a pet fee and have it written into the lease. 

@Luis Martinez I take down info on small things in the beginning when starting the lease like pets names or children's names.

I thought I read an article once which stated that a "whole house" arsenic treatment was required by FHA for all  water in the house, as well as any drinking water for pets or livestock. 

I'll never paint again and I'm rethinking pets 

I was able to rent the other vacant unit for $775 with $25/pet monthly rent.

Think of all the things that could go wrong and see if the lease addresses them: unauthorized pets or tenants, early termination, security deposit, lease violations, late rent, eviction, lawn maintenance, parking, etc.5.