So, how do you know HOW WELL they screened these tenants - if at all?

If you're managing remotely, then finding a software that enables remote showings (if you don't have someone on the ground to show it for you) and you can advertise/screen/place folks from it.

Screened my tenants as well as I could but still encountered endless issues.

The property includes a screened-in patio and an underground pool.

That screen shot is from Hospitable (that’s the PMS I use). $30,441.38 - Thats the “Gross” earnings and includes all taxes (local, city etc) and cleaning fees (if any) and pet fees (if any) etc etc. 

Some minor damages along the way (like a door screen punched out).We have a fenced yard. 

What I do is I continue to screen looking for properties that meet my buy criteria while trying not to be tempted to change my buy criteria just so I can complete a purchase (which is not easy for me).The goal is to make money not to own property.  

They're not the ones who sweated blood into the place, so no offense to management companies, but I can't see going above 10% or 15% at most, assuming nothing major happens etc.I will look into those calculators, thanks, good idea.

Is it bad property management/screening?

My only concern is that the introductory/basic plan has a 5 envelope limit - assuming this is a monthly limitation - and I may have 5+ applicants that are duds before landing on one that I am comfortable with based on screening criteria etc...