Mr. Carroll's arguments are very easily disposed of when one compares fiat paper money. Certainly a gold-standard currency has its problems, but those problems are orders of magnitude worse with a currency not backed by anything. Nearly every argument he makes can be made more harshly upon a fiat/floating currency.
A true gold standard is really a barter system, wherein people trade goods (gold) for other goods & services. If, in the worst case, there is a run on the banks, everyone actually has something: the gold represented by the gold-backed currency. Sure, one may not find a pile of gold particularly useful, but it is infinitely more useful than an ATM card and a "We're sorry, but your banking institution is permanently closed" screen.
Gold is used for currency because it is relatively (but not exceptionally) rare, compact, easily purified, attractive, and generally convenient in relation to currency needs. Silver and platinum are similar, but less suitable due to greater or lesser availability in relation to the desired convenience. The main idea is that the monetary system is actually bartering, instead of a truly abstract representation of wealth. A barter-backed currency could be based on other goods, but gold is by far more convenient; we could have a pastrami-sandwich-backed currency, but storage & durability proves problematic. A floating/fiat currency represents nothing, it is merely an IOU.
Economic problems begin when the gov't starts cheating by handing out more reserve notes than there is gold to back it, meaning that some people are actually holding reserve notes for nothing - a problem exacerbated ultimately when the currency officially represents nothing; a run on banks means people discover they actually own nothing except an "IOU" useful only in scamming the next person into accepting it.
The only good a floating/fiat currency has is, perversely, economic stimulation: it's in everyone's best interests to pass on the IOU notes as quickly as possible in exchange for other goods/services, so that when the music stops they are not stuck with nothing more than a piece of paper (or, more accurately nowdays, a few bits in someone else's computer).
Sure, gold standards have problems - problems which mostly rise from the abuse thereof: handing out reserve notes with nothing backing them, punishing people for owning & marking gold, etc. But fiat currencies are wholly built upon exactly these problems.
I'd like to see an explaination of what's so great about fiat currencies without resorting to gold-bashing.