Indecision on a multi-family property!

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I live in Southeast Michigan and I have found a $69k triplex through a real estate agent's MLS listing that I'm keen on. Two of the units are rented out and one is vacant, which I intend on moving into. I'm single with no kids so that living situation works itself out. Plus, I'm less then 5 minutes away from work!

The house has new flooring, new water heaters, furnaces, and wiring for each unit. So it sounds like the house itself is in pretty good shape but I still need to see the place for myself.

Anyways, I have heard that the area draws poor tenants who are flakey on rents - I work with someone who owns two properties in the same neighborhood and he has had to go to court and fight for delinquent payments, which he ended up losing. So that sounds like a major drawback. Because he hasn't been able to maintain steady tenants, he can't afford the mortgages and he's foreclosing on both. To me, it sounds like this neighborhood is a no-go. 

What are others' thoughts? Does anyone have any general recommendations on assessing if a multi-family property is worth the price, even in a crappier neighborhood?