Looking back over my free will posts, I see that sometimes I seem to be saying that quantum mechanics is important for free will, and sometimes I seem to be saying the opposite. Let me see if I can clear things up.
I have addressed several different issues regarding the free will debate, and quantum mechanics relates to each issue differently.
Determinism and the Consequence Argument: To the extent to which the Consequence Argument depends on the premise of deterministic laws of nature, quantum mechanics is certainly relevant. Since quantum mechanics is an indeterministic theory, if quantum mechanics is a true description of the world, then the Consequence Argument fails. However, we have seen that the fear behind the Consequence Argument is not really the fear of determinism, but of lack of control: If the electrons are in control, then I am not in control. The problem then is not deterministic laws of nature, but any sort of microscopic laws at all.
Predictability: Suppose someone were to write a computer program that accurately predicts everything I will do and say tomorrow. That would be a huge blow to free will (though perhaps not a fatal one). How can I be anything more than a machine if a mere machine can duplicate my actions? Here, I claim quantum mechanics is relevant. Accurate prediction of a classically chaotic system will run up against the quantum limit in a very short time, forcing us to adopt a quantum description. But a quantum description will never produce perfectly accurate predictions: first, because the computer cannot completely replicate my quantum state (thanks to the no-cloning theorem), and second, because quantum predictions are only probabilistic (even if the exact quantum state were known).
Control: Here it gets a bit tricky. We have seen that for me to be in control of my actions, we need a fair amount of determinism in the world. I have been arguing that quantum mechanics has enough indeterminism to make effective prediction impossible. Does quantum mechanics leave us enough determinism for moral responsibility? I suspect it does, but this point clearly needs more investigation.
For now, let me just say that I think the way to proceed is by distinguishing the lower-level and higher-level laws of nature, as I began to do in the previous post.