The seller's agent states that the existing tenant would like to stay on a month to month basis, but has no application from them, they have a small dog (the place wreaks of urine), no security deposit, the owner is the manager without any maintenance records, and the rent is a good $200 month below market.

Just a side note for the title, the house reeked of urine and cocoa puffs...

You can wash everything else with Odor ban or whatever other chemical out there promises to rid urine smell.

I had tenants who had professional jobs and had decent credit who after two years allowed their dogs to defecate and urinate on my nice wood floors. 

The place was completely trashed (some clear vandalism - neighbors saw the teenage son throwing concrete blocks into the pool, urinated on the floor, wrote on walls, and smeared feces on the wall).

v=BZpiieM-gSsAnother tip... with most flooring, it is best to acclimate the flooring product to the room before you install it, as some flooring will react unfavorably to changes in temperature.Pet urine can permanently stain hardwoods, so if you choose real wood be sure to use plenty of coats of protective polyurethane.

The cat urine odors remained.

You think the tenant has a kitty cat (yea I know the urine staining the floor issue) and they denied it.

Revulsion- happens to many first time or fairly new investors, especially those who didn't screen properly, and is when you just can't bring yourself to deal with another tenant issue.Winter evictions, unannounced move-outs, urine and feces soaked carpets, consistent late payments, and incessant petty demands are just some of the issues which can turn the stomach of many RE investors.One thing i'd suggest you do is play out the numbers for various scenarios.

The odor in the garage was unbearable with dog urine and mouse feces.