Enforcing said rulings however, may be a problem. This requires the access of personal information for starters, which currently a large portion of Bitcoin users do not want/like to do.
I would start with standard contracts for currency exchange and online auctions. The contracts would not be more complex than the terms of sites like localbitcoins, bitmit or bitcoin.de.
The arbitration court would have the same role as the escrow service of e.g. localbitcoins.com, except one difference: Our business model is only focused on dispute resolution. Unlike escrow services we never hold any customer's funds, and that's a big regulatory advantage.
Enforcement can be done easily with cryptographic signatures:
a) 2-of-3 multi-signature transactions (slow and expensive, not widely supported yet)
https://en.bitcoin.it/wiki/BIP_0011
https://blockchain.info/wallet/escrow
b) a private key encrypted using Shamir's Secret Sharing (2 of 3 shares to decrypt the private key)
http://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing