From the police report, it seems as if the police are getting called there 2-3 times of day from crimes ranging from Criminal Trespass to shots fired, to even Domestic Disputes in the 4 plex I want to invest in

If I were to lump together all total cases in my jurisdiction, including Domestic Relations and non-contract related disputes that do not touch on the liability of a landlord, the amount would be much higher.

Potential renter with clean criminal background report but googling the person resulted in an arrest for domestic violence by strangulation 6 months ago and an arrest for lewd/lascviousness 10 years ago.  

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If/when they get into a fight, and she's on the lease, he gets the boot when the cops show up on a domestic (he may get the boot anyway the other way, but she won't be able to prove legal residency so easily).

You can typically "domesticate" a judgment in another state under a three seal system.

Since a tenant could die or get out of the lease due to a domestic violence situation, the rent could be refundable.

We don't know if it is domestic violence, drug trafficking, kidnapping, or murder.

I would never put a rooftop garden in the warzone ghetto-- it's likely that either 1) what tenants growing is not edible, at least not food edible 2) some tenant will get drunk and/or violent and fall off the roof and sue the OP or 3) it will be a place where vagrants, drunks, thugs, and lowlifes congregate and either hurt themselves, someone else, or cause some sort of issue for the OP (noise, fights, parties, drugs, violence, juvenille delinquents, skateboarding off the roof, domestic violence, you name it).