Brad does a very good job of summarizing Galbraith's key contributions to economic thought and US policies. He also admits that his influence in economics -- at least as practised in the US -- is almost zero:
Galbraith sees the United States as a would-be social democracy that has lost its way, assuming that if only the self-serving declarations of the right could be wiped away, the benefits of a bigger, more activist government would become obvious to everyone. The right-wing claim that the most efficient economy is one in which the gales of perfect competition scour the land is, in Galbraith's view, nonsense. Modern industrial and post-industrial production is a large-scale process, large-scale processes require planning, and planning requires stability -- which means that the gales of the market must be calmed.
This political vision, however, has been in retreat since the early 1980s. Nobody wants to hear about the importance of Big Government, Big Bureaucracy, or Big Labor (which hardly even exists). Galbraith's economic views have undergone an even more distressing eclipse. Among economists (excluding economic historians), the 70-year-olds have read Galbraith and think he is very important; the 50-year-olds have read Galbraith and know that the 70-year-olds think he is important but are not sure why; and the 30-year-olds have not even read him.
A few paragraphs later, Brad says:
Parker also has an explanation -- also a relatively convincing one -- for the eclipse of Galbraith's economic thought. The story here is of the blindness of an academic establishment steeped in Paul Samuelson's Foundations of Economic Analysis. Economists, Parker believes, have sold their birthright for a tasteless pottage of mathematical models. As a result, they can say much about theory but little about reality. And they ignore Galbraith because he is a guilt-inducing reminder of how much broader and more relevant economics can be.
[...] Nearly all economists today are Paul Samuelson's children. Many are Keynes' children. Friedman, Robert Lucas, Robert Solow, and James Tobin all have plenty of descendants. But there are few Galbraithians on the ground. [...]
Also, do take a look at Paul Krugman's review of Galbraith's The Good Society: The Humane Agenda, to see how a modern -- and highly regarded -- economist views Galbraithian ideas and ideals.