But he writes nonsense. What did he ever get right? Besides the obvious point that "we learn language by copying sentences" can't explain where new sentences come from.

Absolutely not. But linguistics seems like a legitimate enough field, and Chomsky is considered rather influential there.

His work seems to follow logically from Wittgenstein's point that a lot of philosophy comes down to the precise meanings of words.

Ignore his politics, though I personally have a great deal of respect for people with extreme politics.

The Chomsky hierarchy -- a method of classifying formal grammars. Seems computer science-y enough that you'll consider it as something real. http://en.wikipedia.org/wiki/Chomsky_hierarchy