1) How do we deal with the fact that an Internet mob can horribly damage a random individual?
This is a really serious issue. Even a single stalker can cause a nightmare for a person and they will have difficulty fighting back. An Internet mob can be completely devastating. There needs to be some way for an individual to cost effectively fight back against online "assault"--especially when it's a mob.
2) How do we deal with the whole "stochastic terrorism" problem?
Stirring up a bunch of people until finally one of them does something horrific and then sitting back and saying "But I didn't say to go shoot them, I only posted their picture and name with cross-hairs." needs to have some penalty. We didn't used to care about this because only the truly powerful could say "Will no one rid me of this meddlesome priest?" and have grievous harm come about. Now, with the Internet, you can be much less powerful and have your words reach far more people--some of whom will be sufficiently disturbed to carry things out.
3) Facebook and Google are effectively monopolies. How do we deal with that?
We have historically dealt with monopoly by forcing breakups. The lack of monopoly actions in the last several decades has brought us to where these behemoths have no fear.