I think true inflation (and by that I mean take the median person according to average income in the US and look at the dollar weighted prices of the product and services they consume) is higher than the official 2% or so rate. I'm not sure how much higher, but some large components seem to be increasing faster than that including housing, education, medical insurance, and gas. Admittedly there are some important categories such as information, computers, and electronic computer goods that appear to have declining prices.
I would personally guess true inflation is closer to 4% than 2%, though I have to admit I haven't formally or quantitatively measured this so it could be wildly off the mark. Some economists believe true inflation is less than official inflation, for example.
In any case, I think inflation -- and changes in inflationary expectations -- are important in the following scenarios. If inflation is unusually high or unusually low (however you define that), it can alter consumer and business behavior. It can cause very massive shifts in asset allocation, for example from stocks into real estate and gold, or from long term bonds into short term bonds, etc, or vice versa. The true damage is not just major asset allocation changes that are related mostly to the money supply as opposed to the rest of the economy, but also it can create many inefficiencies that reduce productivity -- and that is where the true impact on real wages comes from.
This includes first and foremost higher transaction costs. Whether wheelbarrows full of money in extreme cases, or simply having to spend more time due to second guessing overall prices and their effect on your micro-level transactions, these are addition costs that increase the time and thus cost involved in commerce, without any benefit.
Also, under stable money, it is difficult for businesses to hide lower relative productivity, as the different prices they charge have more accurate levels of measurement. However, when overall prices are fluctuating wildly (inflation or deflation), businesses are vastly more able to hide inefficiencies and blame them so to speak on the overall price movements. This allows unproductive companies a far greater chance at surviving, which reduces productivity (and thus real wage growth) compared to a system in which inefficient companies go bankrupt and lose market share over time to more efficient companies (new and existing).
Yet another very important effect, involves the attempt to directly introduce new money supply into reducing bond interest rates. This can have the effect over time of encouraging consumption at the expense of savings and investment, leading to imbalances. The reverse imbalances are possible in the other direction as well.
In other words, the direct implications of changes in money supply are not quite so bad, it is the related consequences of higher transaction costs and more inefficiency that are the real culprits for reducing productivity and thus real wage growth.
