If there is some loan that's not on their credit report, they would still need to reveal that to the lender.That new loan is going to affect your co-borrows credit and DTI. 

They may reveal some valuable information.Be on the look out for deferred maintenance and outdated features.

I've italicized below the phrase from the ORC posted by @James Wise It is very revealing.

QUESTION: What information does/can a paid title search reveal that can't/won't be found relatively simply by searching public information on county websites?

I think they quoted something like $150 to do a title search that would reveal any outstanding liens.

You'd be surprised how many people have their profile public.Sometimes it can be really revealing as to their character.

But you must learn how to deal with this with a smile on your face, an up beat tone in your voice, and the goal of a positive resolution.80 percent occupancy is a possible red flag revealing some type of problems.

In fact, many things will be revealed you had no idea existed.

Begin the relationship on a positive win-win note.As for screening tenants, your reply post suggest your are overstating your thoughts or have been sadly misled.Learning how to have an informative casual conversation with the prospective tenant and then listening more than talking is more revealing than all the paperwork will reveal.

A title search (usually done by a title company or attorney, but lay people who know their way around the records office can pull their own) will reveal any recorded liens on the property.