On language, human language has intricate rules that we can't fully explain in terms of the underlying neurobiology. But Chomsky's assertion that this implies some sort of underlying mechanism in the brain strikes me as excessively reductionist. Maybe neural networks are inherently capable of learning arbitrary rules, and the kinds of rules that comprise natural languages are constrained not by the brain, but by something else, e.g. maybe only some kinds of grammatical rules are stable over time as languages are subject to random drift.
On politics, Chomsky gives a very thorough critique of US foreign policy, but it is excessively materialist, i.e. it assumes the main driving force in politics is money and power, not ideology. Often this seems far fetched, e.g. US politicians are clearly very eager to please the Jewish lobby (e.g. AIPAC) but according to Chomsky it's the Jewish lobby that has been co-opted by the US in order to use Israel as a tool for US foreign policy. And yet in all the private discussions of all US presidents, all we hear is them being pushed to the right by the Jewish lobby. We never hear them saying "the Middle East is too stable, Jews and Arabs are starting to form solidarity and oppose US imperialism. Quick, pressure Israel to take a harder line".