Some thoughts:
Paper currency of all countries is serialized, so this is not limited to the USA, however, some of these serializations can have common "address space" so you may need to designate Billets, Papier Monnaie, Banknoten, Papier Geld, Cartamoneta, Banconota, Shihei, Okane, Banknotai, Popieriniai Pinigai, Banknoty, Bumazhniye Den'gi, Notas de Banco, Papel Moneda, etc.

Check out http://store.banknotes.com/home.php

The risk of using domestic money of the country you are in, is that this can be confused easily or "borrowed" by someone who sees it as a fungible piece of currency. "one dollar bill is as good as another, why are you screaming?"

Foreign currencies are immune from counterfeiting laws as they are legal tender of another geography.

What might be interesting is to take a defunct paper money currency and imbue it with bitcoin value to resurrect it.