Verify their references, income, and rental history to be sure they will be dependable tenants.

Either direction you go, it would be important to verify their credibility through word of mouth and reviews.

We verify your information via the three major personal credit bureaus, as well as various utility providers.

You also want it to be VERIFIABLE income.  

Just like VG Jason said, do your own due diligence, trust but verify and run your own business.

So, they are more likely to rely on the easy data they find, without delving into the market data more to verify it.

As for work completed, when I had a friend get caught doing work without a permit, he didn't have to pull everything out, but had to pull out pieces to allow inspector to verify work.  

And perhaps in that case, I am thinking to offer them cash for keys to vacate the property (After the property is vacated and condition of the property is verified) rather than hoping that this will get any better. 

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

I'm looking for recommendations of specific brands that people verify the do remove easily!