The Signal and the Noise by Nate Silver is a solid book on predictions and probability which at times is a bit weighty, but due more to the subject than anything Silver should have done differently in the writing.
FiveThirtyEight which began in advance of the 2008 Presidential election and has become a go-to place to get political predictions. Silver makes his calls based in probabilities and does so based on looking at a wide variety of poll numbers and factoring in weighting information about those polls. Out of the November 2012 elections, Silver correctly predicted the Presidential winner in each state as well as all but one Senate race (those unpredictable folk in Montana).
The subtitle to Silver's book is Why So Many Predictions Fail — but Some Don't and he notes fairly in reference to his main title that "the signal is the truth. The noise is what distracts us from the truth." In terms of structure, he lays out in the intro that the first half of the book diagnoses problem with many predictions and the second looks at making predictions better, in large part through the application of something called Baye's theorem.
Some of the prediction areas that Silver notes as having room for improvement are below:
Many people felt the real estate plunge of a few years back couldn't occur because they made predictions based on the idea that home loan defaults were much more independent of each other than was the case. In actuality, what occurred is loan defaults turned out to be very much related as a direct result of home values being tied to one another.
Pundits making their calls about political winners based on feeling turn out to often be wrong. As evidence of this, Silver notes The McLaughlin Group and how predictions on the television show turned out to be roughly equal parts right, wrong, somewhat right and somewhat wrong.
Forecasting disasters such as terrorism, hurricanes, earthquakes, foods and influenza outbreaks.
As Silver gets into the idea of improving prediction, he brings up the aforementioned idea of Bayesian reasoning named after Thomas Bayes, which includes considering the likelihood of events in making predictions. Silver also notes that the concepts behind Baye's theorem fit heavily into principles that guide his FiveThirtyEight blog... (1) think in probabilities of things coming to pass rather than just making predictions, (2) make changes to forecasts as new info arises and (3) look for consensus in forecasts (which sounds to me like a Wisdom of the Crowds-related idea).
All in all, it's a fairly heavy read, but a worthwhile one (or at a minimum, a worthwhile skim of parts that resonate) for somebody interested in predictions, why many of them fall short and how they can be improved.