Paper currency has serial numbers so in a techical sense it isn't totally fungible. However, the extent to which people pay attention to those serial numbers is every limited. If the social context changed so serial number scanners became widely used, paper currency would not be fungible by its nature.
Apparently, the serial numbers on Euro notes dispensed in a given official Euro country can be used to identify which country they were produced for (although they're intended to be equally accepted). Irrational as it may be, some people will ostensibly reject notes thought to come from the PIIGS countries.