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So whenever you meet (or communicate with) somebody who owns bitbills check your bills' public address against their bills' public address. If there is significant counterfeiting going on, eventually you'll find a match. Try to redeem both and you'll quickly find out which is real and which is counterfeit (or that both are counterfeit).
I was going to suggest creating a public Google Documents doc where people could enter their bitbill public keys, but griefers could just look at the block chain and pretend that they were holding bitbills that they don't actually own.