Fixing stuff that breaks isn't even among the top three most time-consuming things a self-managing landlord has to deal with.

Sounds like you'll either need his ink (plan for extra $ for a notary to visit the jail) or a court order recorded among the land records (or however it works where you are located for enforcing an agreement pursuant to a divorce/settlement), i.e. court involvement. 

It's got a great overview of many of the metrics real estate investors use, including those mentioned by @Hai Loc, which are among the most important. 

Simplified steps:1) You collect money, put it in your LLC. execute an agreement among the investors regarding interest rate and when it is due.

There are no heirs to the best of my knowledge and there appears to have been a falling out among the late owner and existing relatives.

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Either he/she didn't, or ex-wife failed to execute and return it... so it's time to record the divorce decree and (redacted) settlement agreement among the land records.

It divides the taxes up among the doors (property, not buildings are taxed) and increases cash flow and makes rent more competitive. 

Odds are all the seller will do is get a handyman to get up on that roof and diddle around with his caulking gun loaded with roofing cement among the existing shingles.

I have never seen charges for vacant units allocated among the other tenants but a landlord could write it in that way.