Actually, random banknotes can usually be traced to a specific person, so any DNA traces could probably be linked - there have been experiments that show that majority of non-tiny banknotes are [A] put in ATM [B] given out to a known person; [C] given to a shop/vendor; [D] retrieved by the bank. So, given multiple banknotes, they could reasonably list the identities of people who shopped in that shop, simply by looking at the banknote serial numbers.
That I can understand, but it's "approximate" info on a banknote that probably has a couple of fingerprints. Even if the store had a video-camera, it's gonna be a bit tough to figure out exactly who gave a given $20 bill to the cashier. And since this person is using cash and not a creditcard, all they got is a (usually bad-quality) store-cam of someone that they think is the one who handed a given $20 bill to the cashier... meh, that's pretty fuzzy. Even if I told the FBI that I'm going to the mall and I will spend a $20 bill this Saturday, I think it would still be exceedingly difficult to find the exact bill unless they were tailing me the whole time. In which case I've already been located & identified by the FBI as a person-of-interest within their physical reach, so I'm already as good as dead.
