You might want to look at this NAR document: Right of First Refusal: A Guide for Real Estate Agents

Primarily when downsizing they question your occupancy intent (Claiming primary residence on a fixer upper for favorable LTV terms, with intent to convert to an investment in the short term) but everything can be worked out with proper documentation.

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

This is where a simple, old school paper application/word document will serve you well. 

They also haven't kept records of the original origination documents as far as I can tell. 

The reason I ask if it used to ascertain damage to something on the lot (water/sewer/utilities hookups or something) and you don't have pics and mutually signed documentation from the lessor/lessee upon each tenant's move in prior to your ownership, would you be able to justify a charge upon move out?

If you have any sort of injury you suffered from the military, GO TO THE DOCTOR and document it.

To list on the MLS, you will need a POA signed by the seller, which states that you can sign on behalf of the owner for listing documents and offers, as well as a signed purchase and sale agreement with an assignability and marketing clause."

Hint: check the recorded documents linked to the property.

How ever I do have a problem units are in a small college town and property manager is great but doesn't document the units as well I would like.