Hameroff, the author, also subscribed to the quantum brain hypothesis, along with Roger Penrose; an idea which was widely dismissed as wildly implausible, if I recall correctly. The topic itself is fascinating though.
To claim the brain leverages quantum effects at biological scales is going far but still plausible. But to say that quantum computations are going on in the brain and are expressed at the level of thinking we acheive (evinced by claiming that we are not Turing machines), that is something that would require a lot of data to support (something that this theory sorely lacks). Much of what we know about quantum mechanics and neurobiology would have to be redressed. Indeed if such were true there would be indirect evidence - I expect we would find quantum mechanics, heck ordinary probability theory, more intuitive for example .
Far more interesting are the epigenetic like effects that occur in memory formation.
There are independent arguments for that position, namely that it's quite likely that the brain does not everywhere operate digitally, with well-defined discrete states. And even if it did in a trivial sense because the whole of physics operated that way it wouldn't really help with describing how the brain works (wrong level of abstraction).
We certainly used to think so, not so much any more. http://physicsworld.com/cws/article/news/2003/sep/03/entangl...