As long as there's older-style currency in circulation, a forger only has replicate those bills and not the new hotness... currency only tends to last a few years in active circulation (at most) but I'd assume that many people will still accept a bill from a style printed 10 or 20 years ago.
Generally when there is a major change to a currency (such as the move to polymer banknotes [an awesome Australian invention] in Australia 15 years ago) the old style bills only remain in circulation for a short period, perhaps a year or so.
Within a couple of years, the old style notes become so exceptionally rare in everyday transactions that the presence of one raises eyebrows, and is inspected carefully. While our older style notes are technically still "legal tender", I doubt you'd find a single retailer across the country that would accept it.
Less than that if there's a major disruption that casts doubt on the legitimacy of more than 5% of the money supply.
The classic case was the huge Northern Bank robbery in Belfast, Northern Ireland in 2004 -- the thieves stole around 7% of all the Northern Bank banknotes in circulation (currency in NI and Scotland is issued by banks that possess a license to print money, not by a nationalized institution like the Federal Reserve). It was cheaper for the bank to reissue the entire currency and cancel the old banknotes than to trouser the loss, so within 4 months the stolen notes were worthless except as toilet paper:
Once there's a noticeable proportion of forged coinage or banknotes in circulation public confidence in the currency drops like a stone. At that point, the only option is to recall and replace.
The reason this hasn't happened in the USA is because there are so damn many dollar bills in circulation -- around $829Bn as of 2007. The cost of recalling and reissuing that little lot would be distinctly non-trivial ...
For the classic currency-catastrophe-caused-by-forgery, you need to read up on the Portuguese banking crisis of 1925, one of the biggest currency frauds in history:
That's because there has not been a disruptive change in USD banknotes for a very long time. And it's desperately needed -- their cotton paper notes are just crap.
The Australian switch to polymer meant an entirely new suite of banknotes which bear almost no resemblance to the paper ones they replaced.
At this point there's a decent installed base of automated bill-reading machinery, though. Not that these ought to be sacrosanct or anything, but the cost and inconveniences associated with a rollout of new bills is substantial.
People will complain about anything. Americans have very odd sentimentality towards their notes and coins, as if history itself will be rewritten when a change is made in the present.
The classic example is the penny. Get rid of it! You can still collect them and read about them on wikipedia, you just won't have to deal with them while buying your double cheeseburgers any more.
In Britain they won't. Our bank notes are officially withdrawn a few years after they are replaced with a new design at which point they can only be exchanged for new ones at banks. Even then I think there is a cut off point of ten years or so where you have to take your notes to the Bank of England if you want them exchanged for legal tender.
