Penrose writes lucidly, and while not as engaging as some other pop science writers (e.g. Dawkins) is still easy to read.
However he is also a grossly mistaken man who has strayed far from his own field - a good Mathematical Physicist he may be but he's no Philosopher or Psychologist.
The main argument of the book centres around Godel's Theorem (or rather Turing's formally equivalent version) to show that mathematical reasoning is non-computational.
This basically begins with the premise 'assume that A is the algorithm which can decide if any given algorithm will terminate' and ends with the contradiction 'if A terminates then A never terminates'.
Penrose concludes that therefore A never terminates and that we must have used a non-algorithmic method for telling this ourselves (since A is the best algorithmic method).
However Penrose has misrepresented Godel, the actual conclusion is the falsity of the premise (that there could ever actually be an algorithm which would tell us if any algorithm terminates).
If Penrose is right and A never terminates then he has violated the initial premise of what A does and invalidated the whole argument.
The whole book then flows from this failure of logical reasoning to a far-out theory of consciousness that is highly implausible and scientifically naive.