For pets, you'll have to know which breeds are unacceptable by your insurance carrier for coverage, set a limit on weight and require they show proof of current vaccination and registration.

Our insurance company provided us a list of dogs that they will not permit on the property and will not cover if there is a claim and they are not all big dogs (Jack Russell is on the list), so you have to check with your insurance carrier regarding liability.

Actually they are a problem if your insurance carrier will not insure a landlord for certain breeds.Service dog or not no landlord wants to take the risk with known unstable breeds.

Sure, I can see some expense in advertising your place for rent however its not like its a wireless carrier charging you an exit fee because they incur fees to give you a phone at a discounted price. 

Talk to your liability insurance carrier about that beyond what the initial inspector says.

. - I kind of (have to) agree with @Bob Bowling here.Also, assuming the tennant is "using/selling meth", "shoot up his building dealing drugs", or "ODs on something in the unit and no one notices until they smell the decomp" is unfair.It would be like you renting a place...your landlord walks in and sees your 6 mo old baby strapped to a carrier while you are outside getting the carseat ready.  

@Josh Carriere when I advertise the unit, I tell people what utilities they must pay (usually for single family homes they pay gas, electric, water, sewer, trash, and plowing). 

Your insurance carrier will provide you a list of breeds it won't allow.

Grand Air division of Carrier.

That includes legal defense fees to be paid by their insurance carrier.