How useful have growth regressions been?

Not very much especially after reading the following paper by Jan Hanousek, et. al. (2004):

Replication of two recent studies of growth determinants shows that results are sensitive to the choice of data from which growth rates are calculated, especially with respect to whether economic convergence has occurred. Previous warnings against using data that has been adjusted to increase cross-country comparability to study within-country patterns over time (growth rates) have been largely ignored at the cost of possibly contaminating the conclusions.

In other words using data from Penn World Tables is incorrect. From the paper:

Heston and Summers themselves state:
PWT has been used by many researchers to measure countries’ growth rates, unaware that the rates they obtained are not the same as the rates implied in the countries’ own national accounts. Both sets are weighted averages of the growth rates of GDP components, but the weights are different.... When told this, a number of growth researchers reacted in a predictable way: since they were indifferent as to [which] growth rate they were using..., this clarification was entirely disregarded..

Nuxoll (1994):
The growth rates in the Penn World Tables do differ from national accounts. International prices are useful for adjusting GDP estimates for differences in price level; they are certainly preferable to using exchange rates. However, using domestic prices to measure growth rates is more reliable, because those prices characterize the trade-offs faced by the decision-making agents, and hence they have a better foundation in the economic theory of index numbers. Probably the ideal is to use Penn WorldTable numbers for levels and the usual national accounts data for growth-rates.

From Hanousek et. al.:
As an indication of the lack of impact of the series of articles pointing out the problems with growth rates derived from the PWT data, although Nuxoll’s paper appeared in the leading professional journal in economics, it was cited in only five of the literally hundreds of empirical cross-country growth studies between 1994 and 2002.

Predictably, this paper was not published in a "leading" journal. Folks like Barro, MRW, etc. really don't like to be told that they have been wrong all along.

While there is some concern for comparability across countries, economists have not really paused to think (or perhaps they over-thought the problem) - If I live in a country in the economists' sample would I be interested in knowing what factors cause my GNP to grow in terms of my local currency or some abstract price-comparability exchange weighted terms? The obvious answer (to me, at least) is that I don't really care about my GNP denominated in some abstract way - I care about it on my terms, i.e. local currency.