With regards to further reading, you can look at Hawkins' most recent (that I'm aware of) paper, "Towards a Mathematical Theory of Cortical Micro-Circuits". It's fairly technical, however, so I hope your math/neuroscience background is strong (I'm not knowledgeable enough to get much out of it).

You can also take a look at Hawkins' company Numenta, particularly the Technology Overview. Hierarchical Temporal Memory is the name of Hawkins' model of the neocortex, which IIRC he believes is responsible for some of the core prediction mechanisms in the human brain.

Edit: I almost forgot, this video of a talk he presented earlier this year may be the best introduction to HTM.

Intelligence-as-prediction/compression is a pretty familiar idea to LWers; there are a number of posts on them which you can find by searching, or you can try looking into the bibliographies and links in:

• http://en.wikipedia.org/wiki/Marcus_Hutter
• http://en.wikipedia.org/wiki/Hutter_Prize
• http://en.wikipedia.org/wiki/J%C3%BCrgen_Schmidhuber

(I have no comments anent On Intelligence specifically. I remember it as being pretty vague as to specifics, and not very dense at all - unobjectionable.)