Determine your screening process from what website you use for background, credit and criminal checks to verifying employment etc.  

Look for red flags such as past evictions, unpaid debts or any criminal records.Conducting an interview: Schedule an in-person or virtual interview with the tenant.

At that point it's called criminal trespassing.

As pet lovers ourselves, we typically like to meet your pets at some point in the process, too.Our tenants’ safety and the peaceful enjoyment of their home is important to us, so we do a credit/criminal background check on all applicants aged 18+.

Yes, that could very well lead to legal/criminal problems.  

That triggers any clause you have regarding police or criminal activity.

Maybe none of them make enough alone, and they have a reasonably amount of other debt, but together they make more than 5x rent, all credit is great, and no criminal or eviction issues.

And if the community backs him, what are they saying about criminals in general?

An Umbrella policy may offer additional legal protections but nothing will protect you from criminal charges, which is a fairly rare occurrence in REI, unless you are a very shady character. 

@Sterling WhiteI do not, I am speaking strictly from criminal statistics, and close friends who are police officers in some of those neighbors and some of the issues they deal with.