Given the number of network connected machines that cash passes though (ATMs, ticket machines, counting machines, ...), I'd assume that such machines would be routinely scanning the serial number of each note. Couple that with an account number, or the CCTV that is usually pointed at any cash handling machine, and I'd posit that the anonymity of cash is eroding.

Well, not really everywhere. If you tried to buy an airline ticket with cash, you'd be subject to a lot of scrutiny.