What's unfortunate is that it's taking the form of a dystopia. Instead of realizing that humans are a factor of the equation, and people doing business in God faith... We're entering a ruthless period where anything goes, and because it's all anonymous no one feels bad about it.
There's crazy potential in the ideas here, but it's way too Wild West.
Not possible without proof-of-work
All they need to do is show two coflicting blocks signed by the "approver"
Decentralization denies the nature of courts. Courts exist to do those things that the market and the mob cannot. Heaven help the litigant who, while in all reality an upstanding person who has done no wrong, must now have his fate decided by popular vote. Why bother with laws. Just put every issue to the vote and let the one with the most twitter followers win.
Courts are where we go when democracy fails. They are where you go when what you want isn't necessarily what everyone else wants of you.