Brian Caplan made a great observation last week, namely that right-wing economic thinkers tend to really love Frederick Bastiat while those more on the left don't. Then in a second and much worse post, he kind of posits a broad conspiracy theory as the reason. To me the second post is emblematic of exactly what I think is unimpressive about Bastiat namely that, much like Caplan, at key points Bastiat seems to me to be assuming what he's trying to argue for. At the same time, he's a great writer with a flair for a great turn of phrase. So if you already agree with what he's saying, you're likely to find quoting or referencing him amusing. But if the goal is to actually persuade someone of something, his writing is pretty unimpressive.
The best example of this is probably "The Candlemaker's Petition" which is a pretty hilarious satire of rent-seeking. And obviously rent-seeking is a real thing, worthy of being satirized. But there are no political controversies for or against pure rent-seeking. The candlemakers' petition is a devastating satire of pharmaceutical companies' endless lust for patent rents, unless you happen to think that pharmaceutical patents and the monopoly rents they generate are a crucial engine of R&D funding and life-saving research. Are the pharmaceutical companies right? I think it's questionable, but I also don't think you'll find the answer in Bastiat.
Similarly, Bastiat's alleged broken windows fallacy involves simply assuming that there's no such thing as genuinely idle resources or an "output gap." In that context, yes, it's a vibrant intuitive depiction of crowding out. But this doesn't counter any Keynesian or monetarist points about the viability of stimulus during a recession induced by nominal shocks, it involves assuming that no such recessions can occur even though they plainly do. In defense of Bastiat, at the time he was writing the modern industrial business cycle was a very new thing and the vast majority of economic ups and downs were caused by things like bad weather which—as you can see in the corn futures market today—is indeed a decisive consideration in an agricultural economy. But that's no excuse for people sitting around in 2012 to be pounding the table with an old book that's non-responsive to modern issues professing to be baffled why people don't find it more persuasive.