I am very supportive of the idea to popularize big scientific thoughts and achievements so that the broader public gets a glimpse of what is being mulled over in the head of those big shots. But I am totally allergic to oversimplification at the expense of the real message.
Why does quantum physics supposedly end the free will debate? You guess it: because with Newtonian physics everything, every thought, every move you make every step you take was in principle predictable. The world was supposedly completely deterministic. You would just have to know all the parameters of the universe at the time of the big bang, then calculate and calculate until you arrive at your phase space of now and, voila, you could extrapolate into the future of your tremendously boring life.
Now quantum physics has added some dice to the system - much to the annoyance of Einstein - (Mr Kaku mentions Heisenbergs uncertainty relation), and with that you get rid of predictability, determinism is out and free will is in. According to Mr. Kaku, Heisenbergs principle tells us that an electron (for example) could not be pinpointed, it could be anywhere at any time. This sounds great but it is an oversimplification and wrong. Quantum mechanics deals with probabilities. It is not true that an electron is a wavefunction. The probability to find an electron at a specific point in space is *described* by a wavefunction. The result may be that the probability to find it anywhere in a given box is equal at any spot - but that does not mean that it is actually everywhere at the same time (the probability to win big in Lotto is equal for any combination of allowed numbers but that does not mean that any combination actually wins - you get it, I assume).
And even if you allow for unpredictability - why exactly does that explain Free Will? Is the lack of predictability equivalent to free will? Is white noise the same as free will? Is randomness free will? Is free will erratic? Is the concept of determinism in contrast to free will? It is very much likely that I will go and have a beer tonight - but I tell you this is my absolutely free will, albeit terribly deterministic.
(there is an anecdote on Mr Kaku's skills of drawing a giraffe that you should not miss)