We could sign the serial number of a 1 Dollar-note together with the value of the bitdollar and maybe a expiry date and print this signature as qr-code on the dollar-note. Everybody could check this signature offline with an android phone. This should keep someone from faking the BitDollar. The private key could be printing as qr-code under a scratch field on the bitdollar. Or without private key and scratch field, the bidDollar should only convert online in real Bitcoin after the expire date (to prevent double spending).