Eric Bickel wrote two papers about weatherman calibration- 2008 paper and 2011 paper. They're well-calibrated for some kinds of predictions but poorly calibrated for other kinds of predictions, and they also tend to have no skill at making predictions more than ~5 days out.
Nate writes well of interesting things, but that meteorologists are calibrated is not new news: the 2001 anthology Principles of Forecasting includes it many times, and they're one of the standard examples of an area in which it is possible to build up genuine expertise because of repeated objective feedback.
There's a way to circumvent the NYT firewall that's easier still than all the ones mentioned so far. Wait for the article to show on your browser, then press the stop button. This will prevent the pop-over from appearing.
The easiest way to get around the limit is to paste the article URL into Google (or if that fails, search for the title.) If Google is the referrer, you are not subject to the limit.
Nate Silver of the New York Times's political prediction blog fivethirtyeight has posted an excerpt of his upcoming book on predictions in various disciplines, The Signal and the Noise. The excerpt describes how meteorologists, in contrast to prognosticators in other domains, have substantially improved the accuracy of their predictions by understanding the limitations of both intuition and computer models, enabling them to combine them intelligently rather than relying excessively on one or the other.
The excerpt is available at http://www.nytimes.com/2012/09/09/magazine/the-weatherman-is-not-a-moron.html?_r=2&pagewanted=all, and a summary is available at http://fivethirtyeight.blogs.nytimes.com/2012/09/09/why-weather-forecasters-are-role-models/
Side note: if you are running up against NYT's 10 article per month limit, opening the links in Incognito Mode will get around it.