The power of the network: For doctors and cops

Networks create value. It's the lesson of Reed's Law (Group Forming Network Theory, see resources) and one which is repeatedly being demonstrated by the success of numerous social networking sites.
Ubiquity, allowing the constantly connected community, makes the value still greater.
And often it seems we talk about the business benefits of this model - the way it enables a new ecology of co-creators - converged prosumers (see Media is the New Way of Doing Business).
But there are other, more transparently beneficial, areas the same thinking should be applied to.
I'm thinking of the medical profession, police forces - education, too?
Anyone going through medical treatment will know you'll see a succession of highly trained individuals. Typically you'll have to describe your symptoms over and over. Typically it gets written down on paper. And while professionals within a department or even at a certain strata within that department, may discuss case studies, they won't connect with others on the other side of the same hospital (or even 'above' and 'below' themselves) - who may have seen the same patient previously or learned something useful from another experience with a patient.
Imagine if doctor A had shared with doctor B about patient X. And symptom Y rang a bell for doctor B because he'd shared with doctor C on a previous occasion. Simply, allowing for emergent intelligence in the network should result in more accurate, swifter diagnoses. That cuts costs for the medical service and heals the patient faster.
Win/Win - new value created by the network.
If networks of professionals beat the best individual professional in predicting the stock market (see Reingold's Smart Mobs), shouldn't they also be better at healthcare? At policing? At educating our children?