For a while, I've tried to avoid the common economic usage of calling the change in an observed variable, minus inflation, the "real" change. I prefer a more neutral and descriptive term like "inflation-adjusted."
What we call nominal quantities really are real, in a sociological sense: they exist, they're directly observable.Your mortgage or car loan requires a schedule of payments in dollars, in some fixed proportion to the value (also in dollars) of the original loan. Those are actual numbers you can see in your contract. The S&P 500 index is at at 1,286; a year ago it was at 1,282. Those are actual numbers you can look up in any financial website. You paid $2.50 for a tube of toothpaste; the bills and coins actually changed hands. Whereas the "real" values of all these numbers are constructions, estimated after the fact (and then re-estimated), involving more or less arbitrary choices and judgement calls. There's no fact of the matter there at all.
To begin with, you have to choose your price index. It's often not obvious whether the consumer price index, the GDP deflator, or some other index is most conceptually appropriate.  And it makes a difference! Just among the most important published price indexes, we see the increase in the price level over the past 50 years ranging from five times, to nearly eight times. Anyone who tells you something like, a dollar in 1960 "is equal to" 13 cents in 2010 is confused, or at least grossly simplifying.
And then there are the differences that don't show up in the published indexes. The CPI is intended to be a price index for all urban consumers, but not every consumer is urban and not all urbs are equal. Robert Gordon estimates that the bulk of the college wage premium goes away if you correct for the higher cost of living in areas where college graduates live. Of course this only makes sense if college grads have to live in pricey urban areas in order to get their college wages. If you instead assumed that the cost of living is higher in urban areas because of various non-market amenities, which college graduates have a particular taste for, then Gordon's correction would be inappropriate.  So again, while nominal values are real, in the sense that they observably exist, "real" values depend on assumptions about various unobservables.
And then there's the after-the-fact adjustments which price indexes are always subject to. (As are nominal aggregates, to be fair, but to a much less extent, and almost always due to better data rather than conceptual changes.) That was what got me thinking about this today, in fact: rereading Dean Baker's comments on the Boskin Commission.  Dean points out that if you take the Commission's methodology seriously, you'd have to make even bigger downward adjustments to inflation in earlier periods, implying that when people in the postwar years thought the economy was threatened by inflation, it was "really" experiencing deflation:
If the size of the current annual overstatement [of the increase in the CPI] is 1.1 percentage points, the the annual overstatement may have exceeded 2.0 percentage points in past years, meaning that, at many times when there was public concern about inflation, the economy was actually experiencing deflation. ... Extrapolating the commission's adjustment backwards implies that, throughout the 1950s and into the 1960s, prices were actually falling. This was a period when the president appointed a council to set wage-price guidelines to keep inflation in check.It's a problem. Obviously using just nominal values is deceptive in many cases, and there are plenty of cases where deflating by some standard index gives a more meaningful number. But one shouldn't suppose that it is "real." And certainly one can't suppose, as the formalism of economics implicitly or explicitly does, that there are quasi-physical quantities of "utility" out there which the appropriate price deflators can convert dollar values into.
We have to think more critically about how the categories of economics join up with social and individual reality. Where goods exchange for each other in markets, they have a quantitative relationship: so much of this is, in some sense, "the same as" so much of that. (There's a reason why Capital Volume I begins how it does, tedious as people sometimes find it.) But that relationship comes into existence in the process of exchange, it didn't exist until then. So as soon as we are talking about goods that don't exchange for each other, say because they exist at different moments, we can no longer regard them as being quantitatively comparable. In this sense, nominal figures are real, since they really describe the quantitative relationship of some stock or flow with others existing in the same pay community. They are observable and are have direct consequences. Not so "real" figures, which depend on the implicit assumption that the only point of contact between the economy and human reality is the mix of goods that is consumed, and that there is a fixed consumption function that converts that mix into a quantity of utility. Without that assumption, there is no basis on which to say that two baskets of goods that can't be traded for each other have any definite quantitative relationship.
Labor might seem to be a better universal standard than utility. There's a reason Keynes made employment his standard measure of economic performance, and wanted to measure output in terms of wage-units. (And it's certainly not because he thought the problems with capitalism originated in the labor market.) And there's a reason why Adam Smith subtitled his chapter on "the Real and Nominal Prices of Commodities" (I don't know how far back the distinction goes, maybe he made it first), "their Price in Labour, and their Price in Money." Well, I don't want to get into the labor theory of value here, except to say that I don;t think any other standard of "real" quantities is any more securely founded. My point is just that it may be, for questions we cannot answer with dollar values, there is no better, objective set of values we can use in their place. At that point we have to think about the various complex ways in which the system of monetary values interacts with the social reality in which it is embedded. For instance, the ways in which the costs of unemployment are not reducible to foregone output and income. The reproduction of society, let's say, has quantitative, law-like moments; those moments are greatly distended under capitalism, but they still aren't everything.
I'll keep on adjusting nominal figures for inflation; what else can you do? But let's not call them real.
 It's worth noting that writers in the Marxist tradition are often more sensitive to the differences between price indexes than are either (Post) Keynesian or mainstream economists. The possibility of a systematic divergence between the price of wage goods and the price of output as a whole was a question Marx gave a lot of thought to.
 I.e., the premium on urban areas implies there's some desirable thing there that's not being measured, but is it a consumer good or an intermediate good?
 Not for fun, for course prep, for my macro course, which I'm hoping to make fodder for blogging this spring. Thus the tag.