That mean that she has a severe mental condition, (bipolar disorder, major and chronic depression, severe eating disorder ect. ) she then has to demonstrate that the cat performs a service that helps her condition.

This would be a pain for most property managers to deal with, at least in the way you describe. 

Many times landlords find some tenants hard to deal with and wished they had them on a month to month rental agreement, because they maybe controlling, or a pain in the rump,  always complaining. 

The owner being a pain could work out in your favor since he isn't cooperating with anyone else trying to see it.Many people will submit an offer on a property without ever seeing it just to get it tied up, as long as you have an inspection and financing contingency, you can always back out. 

I have always approached any type of sales position with the goal of becoming ones friend and advisor to genuinely help the client on their pain points and solve their problems.Due to my lack of personal experience right now asking questions like "are you aware if the title has a lien on it" etc are not natural to me yet and I need to form some type of structure at first to ensure that I do not go through a call thinking everything is great and I have touched all the points only to hang up and realize I didn't ask them how much in repairs they think the place needs, or how old the furnace is etc.

@David Silva With that said...I would also take the time to screen these tenants a little more and see which are 'good' vs. which are 'bad' just like any other tenant.Section 8 can be a pain in the neck to deal with (I have one tenant on section 8 myself) but in the end you get direct deposit into your account and the difference (a small amount) is usually covered by the tenant.

I'd say the nice ones get a longer lease, because filling it again could be a pain.

Forgive the side-track, but I am taking the opinion that you are deciding what level of pain you should feel before paying someone else to take care of the management side for you in exchange for some of your cashflow.  

How do I NOT be a pain in the backside for a contractor?

You would have to invest more in it to qualify, and it's kind of a pain, but maybe once it's rented you could sell it to another investor who wants the guaranteed monthly cash.