He's offering to repair some outstanding issues which are minor.

If a weak credit history, clean up outstanding debt and pay extra security deposit.  

He had outstanding income, and an outstanding job history. 

Over the next few weeks he would like to meet you to make sure there are no outstanding issues or problems.

Anyway, nuff said.Sue:  Sometimes, you can be an outstanding citizen, minding your own business, not putting yourself in a situation where you [should] have to be afraid of [the police].  

In order to use a tenants rent money for anything other then rent, I have in my lease agreement that any money received in my office is applied to any outstanding bills they owe me. 

Then you can apply a rent late fee, since they technically didn't pay on time, as funds are applied to the outstanding balance first.

I have no loans or outstanding debt of any kind.

The two most concerning blemishes to me are the lack of verifiable income and the outstanding debts.

First of all, you should be getting an estoppel certificate, signed by seller and tenant, that outlines current rent, current deposit (even if its $0), and any current outstanding oral agreements.