Apparently it's possible to identify individual pieces of blank paper with the off-the-shelf scanners we already have:
The bottom-line result is a sort of unique fingerprint for each piece of paper, which can be determined using an ordinary desktop scanner.
This means it could be possible to create paper currency that could not be counterfeited- possible for a lot of people to make such things! Of course, the original problem of paper money still stands; it has no intrinsic value, so the value must come from a promise to redeem, unless you are the government and you can just coerce if anyone does what you don't like.
I do think coins, or anything made out of something that had enough intrinsic value, would be a better outlaw currency, and it seems plausible that a similar method of verification could be developed for coinage. Theoretically, circulation would be much less centralized, and therefore, harder to destroy.