I think Tyler is too kind to the critics and concedes too much. I would drop three of his four points in reply and focus solely on his second point, "The alternatives to neoclassical economics, if implemented on a large scale, would be worse." This is a version of Winston Churchill's famous--and devastating--reply to critics of democracy, "Democracy is the worst form of government except for all those others that have been tried."
Or put less elegantly: what have you got that's better? Show me a social science that yields more insight, predicts better, and has more influence, and I'll take broad criticisms of economics more seriously.
On the last point, influence: ask a first- or second-year law student how profoundly economics now affects the study of law. Or ask a business student. (For readers with access to a university library, I can recommend Edward P. Lazear, "Economics Imperialism," Quarterly Journal of Economics, February 2000.)
I am not suggesting that economics is above reproach. I am claiming that too many critics focus on its relatively small shortcomings and tend to ignore, or under-appreciate, its great strengths.