They have an unauthorized animal that is potentially causing damages that may cost you hundreds or thousands of dollars when they leave, and they completed renovations on the home without permission and without following the lease or the law.

We require that we meet the animal, and then charge $150 non-refundable fee, and we raise the rent $50 per month.

No appealing characteristics at all, but it went fast. 

The way I think about it is, "Will the animal due damage to my unit."  

You can ban smokers, pets (but not ESA/Service animals), multi-generational families (with two rooms, there isn't space for grandma and the kids to move in).

Animals? 

She mentioned something about "discrimination" and I cheerfully told her that the person I was going to rent to was also a Section 8 tenant that also had the exact same characteristics as her.

How many animals?

When you're asking questions of whether or not you can charge a pet deposit for a service animal....Or are you required to pay interest on security deposit and when is it enforced....?

By the way, if there is any way you can just rent to grad students - preferably med students or law students or engineering students - just not art or theater majors (party animals!)