That summary is 100 pages long (31,547 words). I'd recommend trimming it down. I hadn't looked into this much before, but was quickly able to find a study repeating my concerns:

All these theories have in common the distinction between cognitive processes that are fast, automatic, and unconscious and those that are slow, deliberative, and conscious. A number of authors have recently suggested that there may be two architecturally (and evolutionarily) distinct cognitive systems underlying these dual-process accounts. However, it emerges that (a) there are multiple kinds of implicit processes described by different theorists and (b) not all of the proposed attributes of the two kinds of processing can be sensibly mapped on to two systems as currently conceived.

- Jonathan St. B.T. Evans

I haven't read the book, but the dual-processing theory itself comes across to me as tautological. I look at the evidence often presented and think they're arguing: if somebody gets the right answer, they must either be using System 2, or the right answer must be a part of System 1. If somebody gets the wrong answer, they must not be using System 2. Just skimming your review, I got the impression you were just attempting to describe the book, and not being very critical of its arguments. In particular, I couldn't find any discussions of the empirical evidence. What do you think are the most important studies which either support or hurt this theory? What sort of studies do you think need to be performed to really say whether this is a good accounting of human reasoning? What would cause you to decide this theory is wrong?