He argues his point very well. There is much more to the brain than the strong AI viewpoint gives credit. They believe that all functions in the brain can be mimicked on a computer. If the brain were solely a bundle of neurons and the only action it relied on were the spikes that are sent down the neurons, then yes, the brain is computable. On the contrary, there is much more to the brain than spikes.
Brain plasticity is one such area that helps in the functionality of the brain.
These many quantum level processes cannot be computed and the brain is implied to be non-deterministic. Penrose's book brings up many excellent questions that may have been taken for granted. He uses many traditional examples, such as Searle's Chinese Room, to explain understanding and consciousness. The strong AI front believes the brain is computable, thought is computable, but this would rely on the spikes alone. There is no way to compute the inside of the body of the neuron, brain plasticity, or even neuron creation if quantum mechanics is found to govern these functions.