The big thing I got from this chapter was that there is more to support the notion that most of the differences between human and animal cognitive abilities stem from the size of the human brain as opposed to its quality.
The evidence cited for differences in human vs. animal brains seemed fairly slim by comparison - from a structural standpoint it does not sound like there is a whole lot of differences between human brains and other primates. The differences in proteins also seems rather small.
One area that is completely ignored is that glia cells - the non-neuronal cells in the brain that perform functions such as immunity, neurotransmitter re-uptake and myelination. The book
The Other Brain: From Dementia to Schizophrenia, How New Discoveries about the Brain Are Revolutionizing Medicine and Science describes how these other cells, that outnumber neurons in the brain by more than 3 to 1, appear to do much more than simply provide support to neurons. It would be interesting to learn whether human brains differ significantly from other mammals with respect to glial cells instead of focusing exclusively on neurons.
The part at the end of the chapter about Boskops seemed out of place with respect to what the rest of the chapter talked about. Furthermore, the discussion does not mention Neanderthals, Cro-Magnons or other possible sub-species that might have had a larger brain size than modern humans: the discussion left me thinking that the authors considered Boskops to be another sub-species rather than statistical outliers.
The discussion about Boskops does give a very good reason for decreasing brain size, to whit that a larger brain at birth translates to a more difficult birthing process. Given how dangerous childbirth is for modern women, a child with a 30% larger head would pose an even greater risk than existing babies. The loss of a mother is especially bad because it means the loss of an established and valuable member of a society, making a community of large brained individuals even more difficult to support.