They're very complicated, imho, and not much different from any corporation now. The work itself is often derailed by the incessant need to raise funds and cover administrative costs.
I don't know how to fix anything either, but recognizing and bringing the systemic problems to light, and getting our priorities straight as it concerns the gross wealth inequality and where our tax dollars go, would be a good start.
The non-profit world, like Wall Street, is so easily manipulated for the benefit of a few, unfortunately. There are wonderful organizations, but there are so many now that efforts are often fragmented and, again, it's easy for greed to take hold. 
I'm personally more inclined to integrate everything. Why should "doing good" be separate from one's means of generating an income? Social enterprises are doing philanthropic work while simultaneously generating jobs.
Like everything, there are no doubt many different ways to approach a problem -- and we must multitask and deal with the systemic issues while simultaneously taking care of critical needs -- but to leave things as is isn't an option to me.
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