I've been away all day and am a bit surprised to have gotten by with so few flames. I came upon Chomsky from the psychology/learning theory aspect rather than from the computer science or political aspect of his writings. this was about 35 years ago and I have not kept up with the details of his career.
It seemed to me that his assertion that aspects of language were built in to the brain was tautalogical -- of course there must be some underlying structural differences between humans, apes, and other animals -- else we could teach sign language or reading to dogs. The question is whether this assertion adds anything to our knowledge. It seems to me that transformational grammer has been kind of sterile in the realm of human language. I know of no school of psychology that uses any of his ideas in a teaching or therapy setting. I know of no Chomskian school of literary criticism, no transformational grammer of poetry.
The reason, I assume, is that grammer and syntax are rather trivial aspects on language that say nothing about the underlying motivation for talking in the first place. Is there, for example, a Chomskian method for analyzing a statement for its probable truthfulness or sincerity, or humorous intent, or double entendre? Is there a Chomskian analysis of inflection?
I see a parallel in Chomsky's approach to language and his approach to politics. I politics he believes that all human needs can be fulfilled by the application of rigorous logic (from above, of course). Individual will is messy and unnecessary. Emotions are nasty and need to be suppressed.
You haven't missed anything - careerwise, he hasn't done anything worthwhile in forty years. Actually, I once heard it suggested that his problem was premature success - he came right out of the gate with theories on universal grammars, generative grammmars, transformational grammars, and ever since, has been really struggling to duplicate that sort of early success. And so his politics have gradually become more and more outrageous (stupid, if you ask me) in an attempt to keep himself in the public eye. He's done nothing of note in linguistics since the early Sixties - it's all politics keeping the spotlight on him nowadays.
Does his work tell us anything new about human nature? Probably not, but it does tell us useful things about the nature of languages. Now, if you want flames, try praising his semi-retarded political theories. ;)
Actually in the late 1970's Leonard Bernstein based many of his ideas regarding the interpretation of music on Chomsky's theories.