I have been both busy and traveling the last few days and haven't been able to read all of the controversy set off by a Sheldon Richman column on Austrians and inflation, including the back and forth between Scott Sumner and Bob Murphy. However, I have read some of it and I think folks have focused too much on the question of the wealth effects of who gets the money first as opposed to the fact that money takes a particular path means that money affects prices differentially.
What I mean by that is that, yes, a bond dealer who sells to the Fed is just swapping one asset for another (which is also true of anyone who spends money of course), but that particular exchange leads to some banks having additional reserves, which translates into loans (well, normally anyway), which translate into borrowers spending. Those borrowers spend on some goods and not others. Yes, all of these are just swaps of assets, but the imporant point here is not the change in wealth but the impact on relative prices.
Whatever the existence or non-existence of wealth transfers from the injection of new money, it does afffect the array of relative prices, which means it affects the investment decisions of entrepeneurs, which means it affects the capital structure. Given the heterogeneity and specificity of capital, the capital structure cannot be costlessly refit each time a new injection of money occurs, nor when the injection stops and underlying demand and supply reassert themselves. These represent real wealth lost due to the injection/relative price effects of inflation.
Even if we take Bill Woolsey's point that people base price changes on anticipated changes in spending and not actual changes, in an Austrian world there's no reason to believe those expectations will all be identical. Because the money goes to specific places at specific times, people will still react to the changes in the prices of their inputs, say, in different ways, and those different reactions will have real effects on the capital structure and therefore other real variables.
More systemically, these relative price effects increase the epistemic burden on market actors as prices become less reliable signals of underlying consumer preferences and opportunity costs, thanks to the temporary pushes and pulls from the injection of excess supplies of money. People are simply more likely to guess wrong about what a price movement means, and are thereby more likely to make irreversible (at least to some degree) decisions with respect to investments in human and physical capital.
The Austrian understanding of injection effects cannot be separated from its understanding of the price system and capital theory. It doesn't matter so much WHO gets the money first. What matters is that SOMEONE does and that the dispersion across the price system is not even. THAT matters because it ripples through the capital structure with real, not just nominal, effects. The Austrian theory of the business cycle is one kind of systematic real effect, but there can be others.
Again, I haven't read all of this debate, so perhaps Scott and others have addressed this point.