Just yesterday we read about how Facebook 'helps' marketers 'track when people were feeling overwhelmed, worthless or insecure' [1]. Focusing on people that exhibit this frequently, particularly if they're being bullied, would catch a bunch of these online suicide cases without squandering labor on everyone else.
Then all you need to do is invent enough euphemisms to enable a degree of profiling; the rape streams that go unreported for days are almost always gangbangers. Should be a trivial job to factor that group out, by their grammar alone.
There you go; the chronically depressed types and the gangbangers account for probably 95% of the headline making cases Facebook has to worry about. Focus a small workforce on those two groups (and possibly a few others; extremists, etc.) and Bob's your uncle.
[1] http://www.moneyandmentalhealth.org/facebook-mental-health/