Sharing music, video and/or porn on the network will be mostly inevitable. But on the other hand, the web of trust should limit the impact of this alot. If you consider that people interested in curating/helping with the leaks and documents would distrust peers putting porn/music/video up, there will likely be 2 or more networks with little trust between one another.

You didn't mention anything about anonymization of the nodes/peers. I am guessing you're thinking of putting this behind Tor?