Pretty tough neighborhood likely dealbeat/criminals in this one.

So nothing to fear from the criminals themselves.

Be strict on your lease, qualifying your tenants with good credit, 3xtimes rent income, no criminal background. 

What types of services do you use to screen potential tenants, such as credit score, employment, and criminal records? 

Here are a few: Drug related criminal activity occurring in or around leased premises is cause for immediate eviction.

Studied criminal justice but dropped out.

Please note that not all states have additional Fair Housing laws.however, Colorado doesn't appear in the list of linked states, so maybe that's not the case right now for you.This is designed to protect people who receive government benefits (or cannot work and receive assistance), not criminals.

I just make sure they have a job, no criminal backgrounds, and are thinking 6+ months.

Go through each of the criteria to let them know what you will be checking for, if they balk at the prospect of you calling their employer or checking the criminal history, etc, they're probably not going to pay the application fee.I understand you're really asking about the gut feeling aspect but generally, if you have comprehensive criteria for tenant screening, chances are the tenant who doesn't meet your "gut" test won't meet at least one of your criteria. 

This is a REC matter, not a criminal matter.