Or worse yet what if the person is "willing to pay above market rent" because they have bad credit (doesn't intend to pay), no verifiable income (can't pay), or a track record for trashing rentals?

I can only imagine that the certificate programs online are of similar quality.

Cat urine stays even after 1 time , if it was that bad the contractor wouldnt go in , its a BIG problem 

A negative cash flow isn't a bad thing for some investors due to the tax write-offs they get, especially if there's a lot of equity buildup. 

I know stability is fantastic, but I certainly don't want a bad situation that someone has just dealt with or someone who won't accept any rent increases.

In one area it is bad enough that the wall move when you push on it.

Bad ones?

Explain that you will be with the prospective tenant during the showing to ease their mind.They might have had a bad experience with another landlord showing their unit, and sometimes if you explain where you are coming from, they're more understanding.

I'll try to find another to work with, my Realtor has very bad connections (which may explain why he has been struggling as a Realtor lol I'm trying to help him out as I go along, so far he's learning some things from me and I'm more new to all this than he is haha).

A lot depends on the quality of the rental which you didn't address.