While we don't have any rodent/pest issues, this seems like a massive invitation for something to enter my apartment while crawling through the walls of my building. 

I think you are doing the right things by meeting the tenants and that may mean you had an inspection too?

Do you have interest in purchasing larger assets like apartments, commercial strip centers, etc? 

There is some concern about an over supply of apartments in the area.

Listen to your gut.As you said, it sounds to me like she’s trying to rent the condo for her daughter, but her daughter has some sort of stain on her record/credit that impedes her ability to be approved for an apartment. 

The major focus of the work would be to inspect properties both owned and potential acquisitions. 

What if you bought a unit with a 30-year-old millionaire that always paid his rent 15 days in advance with gold bullion and never even occupied the apartment?

It should have the standard contingencies (inspection, clear title, and if needed, financing). 

Set a time for an inspection.

You should likely sell and 1031 exchange into apartments