The social sector has not leveraged innovation anywhere like the business sector has, and there are many reasons for this. Firstly, innovation is not understood - it is often mistaken for invention or creativity, and different people have different notions of what it is.
Apart from this, there is resistance to adopting business sector practices because there is a belief that we are unique (and more complex). There is a tendency to create 'inside-out' solutions rather than solutions that address insights from 'out there' that meet real needs and create wholly new possibilities. There is no urgency to create scale (like the business sector), with the belief that I'm doing good, that's good enough. And often people are not sure how to go about 'innovation by design'.
Here's a nice video link - http://www.youtube.com/watch?v=2NK0WR2GtFs