As with nearly all papers addressing such topics, parts of it look as if they were purposefully written to invite ridicule, as when he presents estimates of 19th century prices calculated to six significant digits. (Sorry for being snide, but what was that about spurious precision in economics being the fault of politicians?)

[facepalm] OK, I'm not making any excuse for that. Given the magnitude of his findings he doesn't even need them to make his point.

The mathematical discussion in Section 1.3.2. seems to imply (or rather assume) that even assuming omniscience, a "true price index" (Nordhaus's term) can be defined only for a population of identical individuals with unchanging utility functions. This seems to support my criticisms, especially considering that the very notion of a human utility function is a giant spherical cow.

Yes, you can't produce a true price index. But less-than-true price indices can still be useful.

Nordhaus considers only the fact that price indexes fail to account for the benefits of technological development, so he keeps insisting that the situation is more optimistic than what they say. But he fails to notice that the past was not necessarily worse in every respect. In many places, for example, it is much less affordable than a few decades ago to live in a conveniently located low-crime neighborhood, and this goal will suck up a very significant percentage of income of all but the wealthiest folks.

But houses keep getting bigger and you have to account for that too. Besides which, housing is no more than a third of most people's income, at least it is in my country. That is a significant percentage, but it's still less than half. And things keep getting better (or no worse) in the remaining two thirds.

More to the same point, unless I missed the part where he discusses it, Nordhaus seems oblivious to the fact that much consumption is due to signalling and status competition, not utility derived from inherent qualities of goods.

Assuming it's even possible to adjust for that, I'd really want to apply the adjustment to GDP, not prices. Signalling isn't a matter of cost but rather value.

Finally, I can't help but notice that in the quest for an objective measure of the price of light, Nordhaus seems to have reinvented the labor theory of value! Talk about things coming back full circle.

No, you're confusing cost and value. The labour theory of value is the theory that the value of a good derives from the labour taken to produce it. If Nordhaus were using this theory he'd be arguing that the value of light keeps falling. Measuring cost with labour is another thing entirely.

Overall, I would ask: can you imagine a paper like this being published in physics or some other natural science, which would convincingly argue that widely used methodologies on which major parts of the existing body of research rest in fact produce spurious numbers -- with the result that everyone acknowledges that the author has a point, and keeps on doing things the same as before?

No. I recognise this is a problem. I can only imagine they thing it's too had to correct for technological change robustly, but that's not really an excuse. If you can't do it well, it's generally still better to do it badly than not at all. And I didn't realise the research was that old (I've actually never read the paper, I read a summary in a much more recent book). Apparently macroeconomists have more catch-up to do than I thought.