The actual Achilles Heel of Bitcoin is the sparse few exchanges that convert Bitcoin to hard cash. If these exchanges can not control price manipulation schemes among their traders then Bitcoin's value will quickly bubble and pop. What Bitcoin needs is to be accepted by an established trading exchange which would stabilize the real world price of Bitcoins.
Bitcoin is an Achilles Centipede; that may be one of its many heels.
Another: is its conflation of efficient transaction medium and store of value, as if the simple "scarcity" of cryptographic random numbers would allow it to hold value once people decide it's no longer a competitive way to conduct business.
You see this in message board debates all the time, where bitcoin supporters, having been talked down from the notion that particularly idiosyncratic bit patterns in SHA256 hashes can ever have intrinsic value, resort to talking up bitcoin's utility as an cheap and anonymous Paypal; then, when confronted by bitcoin's manifest liabilities as a transaction media (for instance, the fact that it's so thinly traded that its price can jump double digit percentage points during the time it takes to clear a transaction), they revert back to the intrinsic value of mathematical scarcity compared to the oogie-boogie Federal Reserve.