When I was in Ecuador (which uses the US dollar) it was extremely common to find fake $20s in your change. I could never spot them, but the locals could.
They were exceptionally good, right down to the watermark, security strip, etc. etc. Even when I had a known real one and a known fake one, I couldn't tell them apart.
They could feel the texture with their fingers (I couldn't tell any difference) and the security strip was a tiny, tiny bit longer than it should have been on the fakes.
Even after they told me what to look for, I couldn't tell.
This is precisely the reason the U.S. Treasury still insists on using natural fiber in paper notes. There's more detail in this delightful Esquire article about the making of paper currency:
Tl;dr: 100$ bills produced in all likelihood by a foreign government (suspects are North Korea, Syria, Iran) or maybe criminal gangs are so well done that they are practically indistinguishable from the original.
The numbers printed seem to be pretty low though, and not nearly enough to endanger the economy in any way. Probably its hard to launder the money?
Rates for the US are around 0.01% of circulating notes.
As far as counterfeit currency being a danger to economies, check out Operation Bernhard [1] where Nazi Germany forged British bank notes to flood the economy, with the goal of causing rapid inflation that would be damaging to the government.
There's a good movie as well, from 2007, about the operation: Die Fälsche (The Counterfeiters) [2]. Definitely worth a watch.
A lot. http://en.wikipedia.org/wiki/Superdollar