I'm just saying cash for keys is rewarding for bad behavior.

Their dog was still living their (without them) up until two days ago...

., @Steve Vaughan, @Dennis WayneI'd want to add that I am not trying to be a heartless landlord but I am starting to get worried that this tenant will expose me to liabilities with their bad behavior.

They've added two dogs (against the lease).

It is easier in that case to say Hey how about you teach me how to do this and I will do some "bird-dogging" for you? 

Party all night, play loud music, literally go bowling on the floor above them, do all your farting in the common areas, get a small dog that never stops barking, etc.

One tenant has a dog and cat in violation of the lease and unit is in worst condition of the 4 because of neglect and the pets.

Rewarding bad behavior feels bad, but focus on your long term success over short term pain.  

I looked around the area and knowing the size of our place, number of beds/baths, plus other benefits such as it being a top floor unit, two parking spots and dogs allowed..

. - Animals must be current on vaccinations (with proof), dogs require a pet interview, animal rent of $25/month/pet and $150 one-time move-in fee for pets- Positive, verifiable 2+ years of employment history.Thanks for your insights!