Bill Woolsey, Scott Sumner (here and here), and Nick Rowe and a debate that was fun to follow. It seems to me that they more or less end up on the same page. Here's my rough synopsis.
The argument seems to have started as a semantic battle over the definition of the word money. Scott holds that money is the medium of account (MOA), Nick and Bill say it's the medium of exchange (MOE). I say ignore this part of the conflict. Pretend the word money doesn't exist.
Scott's point centres around the following example. The MOA in Zimbabwe is gold. This means that the sticker prices of goods and services are set in gold ounces. But Zimbabweans pay for these things using a central bank issued Zim$. Shopkeepers keep a sign at the till showing the current exchange rate between an ounce of gold and Zim$ so people who have bought x ounces worth of goods know how many Zim$ to pay. Say that the demand for gold in China explodes. Scott says that shopkeepers will lower their gold sticker prices in response. If some of those prices are rigid, you can get a recession. It would seem here that shocks to the MOA are doing all the heavy pulling in creating this recession, which is what Scott is trying to show.
The point of contention seems to be this: sure, a fall in sticker prices of things would cause the recession, but why do sticker prices fall in the first place?
If one starts by assuming a Walrasian market then sticker prices fall instantaneously. This adjustment is ensured by the omniscient "auctioneer" who announces prices and clears trades on behalf of all market participants. The change in Chinese preferences for gold is immediately conveyed to Zimbabwean shopkeepers, the appropriate trades determined, and the market opens for business at these new prices and distributions.
But in the absence of a centralized system, how do the changes in Chinese preferences get conveyed to Zimbabwean shopkeepers and trades get cleared? Economies have evolved complex patterns of highly tradeable MOEs that solve these problems. What causes sticker prices to fall goes like this (I'm cribbing this from Bill's post). The increase in the demand for gold in China causes the yuan price of gold to rise. Given the yuan/Zim$ exchange rate, Zimbabwean shopkeepers can infer that the Zim$ has fallen relative to gold. The signs at their tills are updated to show that people must pay more of the MOE to buy the same quantity of stuff.
As a result, the Zim$ that Zimbabweans held in their wallets can't buy as much as before. In order to rebuild their purchasing power they hold off on spending. Shopkeepers have to reduce the sticker prices of their goods in order to attract purchases. Again, if some price are rigid you can get a recession from this. Thus not just the MOA, but various MOEs, the yuan and the Zim$, do some heavy pulling too in creating the recession.
The point of all this is that Nick, Scott, and Bill probably agree on whether the MOA does all the work, or the MOA and MOE combine to do the work in creating the recession, depending on what assumptions one starts with.
Using this model, it's interesting to imagine what would happen if the demand for Zim$ suddenly exploded. Would it cause a recession, given that some sticker prices are rigid? To satisfy the new demand for the MOE, the price of the Zim$ has to rise. Shopkeepers quickly update the signs at their till with the new exchange rate. Sticker prices in the aisles don't need to change at all, so there is no recession. Thus within the framework of the Zimbabwe model, changes in MOE demand are insufficient to cause recessions - a change in the MOA is necessary for the MOE to have recessionary effects. Now if certain shopkeepers who sell certain unique goods are prevented by edict from updating their signs (at the till) fast enough, then it seems to me that you could once again have a recession. But this is because price rigidity has been expanded to include not only sticker prices (the MOA) but till prices (the MOE). Perhaps the important thing out of all this debate is that MOE vs MOA is not the pivotal axis. Rather, what ever you make rigid becomes the pivot.
As for the definition of money, that's probably worth ignoring for now. Money is just one of those words, much like bubble, that probably needs to be thrown out of the economic vocabulary.
PS: Bill Woolsey has a very useful comment here about the definitions of medium of account, unit of account, and redemption media.