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I don't know how often serial numbers are checked, but I imagine that if those bills had been in circulation, they would have been retired by now (banks will take damaged/worn-out bills out of circulation to be replaced). I'm sure that the serial numbers are recorded when bills are taken out of circulation, so if the DB Cooper money was circulating, the FBI would have heard about it.

The bills go through Federal Reserve bank offices. It is possible that a surveillance for such bills are implemented there.

Considering that every letter sent through the post office is scanned, interpreted by computer and stored, it's not unreasonable to assume that serial numbers are at least scanned when they return to the Federal Reserve.

Beyond the police angle, metrics on how quickly money is circulating is probably useful data for Fed economists.