You'll notice as you go South and you research Red States laws are more in favor for Landlords and Property Taxes are more manageable..  

If a prospective tenant is in a rush to move, usually it's a red flag unless they tell you upfront why they need to move.

That is a red flag to me. 

3 red flags:1. 

For example, HAI in one of the markets I'm looking at is 245 . is this a red flag?

I'm rooting for you guys. 

We want the root cause of the problem addressed and the problem fixed for good but we are not sure our property management company can manage this repair and/or stick us with unnecessary costs and/or no guarantee of reoccurence.  

Even caught red handed you would be way ahead and wouldn't have to go through all their non sense permitting process and very likely wouldn't be fined if you retroactively comply with their inquiries.

A few years ago I helped my (retired) parents buy their most recent house by directly giving them a $100k cash down payment, and they would like to leave the house to me when they pass in thanks for the assistance (it ended up helping keep their mortgage extremely low since they are on a fixed income).They are very worried that it will somehow get caught up in probate or red tape when they pass even if my name is spelled out in the will, and wanted to see about just adding me to the title or something so that there is a seamless transition without any hassle.

When your SF is down for renovation or being marketed for a new tenant, you have $0 coming in but you still have a mortgage to pay, so the month is automatically in the red, not even counting any other expenses, etc..