Bennett McCallum is one of the most accomplished monetary economists of the past few decades. He also happens to be a champion of nominal GDP targeting. In a paper he did late last year for the Shadow Open Market Committee he discusses some of the problems with inflation targeting. He notes that even if one takes inflation targeting to be of the Taylor Rule type--where there is both an inflation and output gap term--there are still problems with it:
I would myself argue that the most prominent form of a typical IT policy rule, as described above, has a weakness stemming from its inclusion of the output gap as a second target/indicator variable to respond to. In particular, measurement of the “gap” requires measurement of the “natural rate” of output; but the latter is an unobservable and unmeasured variable that is conceptually different for every different specification of price-adjustment behavior used in the adopted macro model. And the price-adjustment relationship is arguably the single weakest and most-disputed portion of any macro-econometric model! For this reason, among others, I have long believed that use of the change in aggregate nominal spending—i.e., the change in a refined version of nominal GDP—would represent a more sensible combination of inflation and real-variable measures than is provided by the two variables of the traditional IT rule.