Apparently, sensitivity analysis (which takes more work) is the researcher's best check for robustness -- there is no diagnostic statistic available as part of the standard regression output.
Most social scientists thing of its use as a bit of a dark art largely because -- at least where I've used it -- the results are fragile (in the statistical sense of that word.) It's easy enough nowadays to run principal components, as Iowahawk shows, but it's also quite easy to change one item included in the list of proxy variables and get quite different results. Any social scientist who does statistics and has used PCA knows this (I talked to as many as I could find when I did the central bank independence and economic freedom papers. Most were not economists, because economists are even more leery of PCA than political scientists or sociologists.) What I did not know was that it was the method used to append the pre-1850 temperature data to the graph. It increases my skepticism to know this was the method they used.
Note, this doesn't make the scientists arguing for global warming wrong; it only means I want to see the raw data and run lots of permutations of the proxy variable list. Not providing that data or, worse, destroying it makes me suspicious, however.
IT'S WORSE THAN I FEARED. King Banaian follows up on my observations about principal components estimators.