Always have counsel you can speak with, don't be a penny wise but a pound foolish; 5.

I do not allow more than one dog over 35 pounds in the same unit, and I do not allow any aggressive breeds.I think collecting a "pet deposit" is folly - since you can only use it on pet damage. 

This takes a LOT of my time.If I went to get a judgement against this tenant for the balance of the lease (if I could even find them to serve court papers), the judge would tell me to go pound sand, absorb it as a business expense, go re-rent the apartment, move on with my life and quit bothering him with this "nonsense."

It will cost you a few pounds in weight though - lol.

Are there ways to attract undesirable tenants?

Penny wise and pound foolish.

Most people who rent a unit with all hardwood floors bring their own area rugs anyway, which should deaden most of the most obnoxious pounding. 

They can weigh 50 pounds and sound like an elephant to me.Funny story - the building I last managed had 10 foot ceilings and was an old very solidly built building with carpets. 

If you pay, then I'll give you this one and tell her to go pound sand.You rented a SFH, normally that would require you to do yard maintenance but she has agreed to mow your lawn.  

It doesn't matter if the man weighed 250 pounds or 350, the owner has a responsibility to provide a high level of safety.