Eye opener. The authors knew they were going full controversial, but were confident to be right. Be sure, it seems to me most of the controversy around the book is linked to a bad effect of antonomasia - just like if you try to criticize the European Union, people may get mad mostly because they equate EU with Europe. In this case, people got and get mad because they equate tout cur evolutionism with (neo-)Darwinism. Well, this book is not against evolution. Evolution is a fact - and it was unquestionably the biggest conceptual innovation of the 19th century because it removed Aristotelian fixed hierarchies from nature. What this book purports to prove is instead that the claim that (all) evolution can be explained by the theory originally proposed by Charles Darwin (and Wallace, always forgotten (perhaps because not British?)) as more recently (saved and) expanded with the inclusion of genetics (the so-called modern synthesis, aka neo-Darwinism) is false, empty. In fact Fodor and Piattelli-Palmerini claim that there is no theory of evolution, and probably there cannot be, and anyway natural selection and adaptationism can at most justify only a part of it instead of being the main mechanism behind evolution.
How they proceed along this if anything intellectually very stimulating path is actually rather simple after all, and in spite of being already rather short the book could have been even shorter (they could have made a synthesis of the arguments upfront), what makes it look like long is the writing style. They start with stating what they consider the essence of neo-Darwinism - and here, it is understood that they risk the straw man fallacy, because people that do not agree on this definition may have arguments to contest since the beginning. They claim that neo-Darwinism explains evolution by envisioning a source of random mutations in the genotypes whose corresponding phenotypes are then filtered by natural selection. According to Fodor and Piattelli-Palmarini this statement, for want of sounding quite right upfront, and in spite of having been repeated ad nauseam for ages, is false and actually empty. The reason is essentially two-fold. The first is that such theory assumes that all changes to the phenotypes are exogenous, whereas this is demonstrably false or at least do not cover all evidence. So the first part of the book describes endogenous constraints on the expression of genotypes into phenotypes, which are getting clearer in time: epigenetics, horizontal movement of transposable elements (transposons), the hierarchical level of structure that control the biological development (so called evo-devo, according to which nothing in evolution makes sense unless in the light of developmental biology), and the even more fundamental physics of complex systems, according to which many structures just cannot be different from what they are because that's how matter does according to existing laws. This latter trend recovers observations from D'Arcy Thompson and Stuart Kauffman in particular. This part is also illustrated with the analogy with Skinnerian behaviorism, which breaks down in an important aspect that constitutes the second part of the argument of the book: natural selection is a void filter because it lacks intentionality, therefore the (Darwin's own) analogy with artificial selection is a misconception. To distinguish among traits that supposedly affect positively the fitness of a phenotype from free-riders requires intention, basically a mind. The reason is that to distinguish the two one needs counterfactuals (Mill's method of differences), but unfortunately counterfactuals cannot exert evolutionary pressure without some mind/intention enforcing it (whereas in a theory of behavior minds are in place, and mental representations were vindicated after the death of Skinnerism). As a matter of fact, once you realize this you start to see (plenty of examples in the book, particularly in the Appendix) that virtually all supposedly Darwinian accounts of evolution are post hoc and based on counterfactuals - this makes the book an eye opener in the first place. They claim that the inference from "X is F and was selected" to "X was selected for F" is illicit in natural selection because it requires an intention that is absent in an explicitly naturalistic theory. The beloved perfect fit to ecological niches turns out to suffer from the same problem, because on one hand adaptation and niche are defined circularly, and on the other is a truism because not finding a niche means death (unless one finds his niche, which the right place to get a living from, (s)he dies). (Lynn Margulis also pointed out - not in the book - that the simple fact that you are living means you are fit; besides, the intervention of minds is per se a huge challenge to the theory, for instance I can decide not to reproduce even after killing everyone else).
So what is left? Well, natural history, as indeed most supposedly evolutionary accounts already are - descriptions of causal chains with eventually some plausible narrative on top. In fact, the book claims that it is really hard to do much more than that, and certainly Darwin could not do it and certainly not in a way that covers all cases.
As I said, the writing style is not the smoothest you'll find (that's big part of the reason I finished reading the book only at the third attempt), and admittedly part of the immediacy of the book is lost in philosophical arguments, some rather technical, that are not palatable to all. However the attitude is still rather colloquial and witty (especially in the notes), which partly compensates for that. The authors own the cited bibliography, and do not particularly restraint from criticizing uber-Darwinians like Pinker, Dennett and of course Dawkins (selfish gene, blind watchmaker... talking about intentionality), which per se is a decent source of entertainment.
A few side notes:
The fact that criticizing (neo-)Darwinism is considered heresy speaks of the current existence of dogmas in science.
Popper's falsificationism as solution to the problem of inference owes a lot to Darwinian thought (though Popper himself stated that Darwinism cannot be tested), and the heuristic validity of his theory remains intact even if Darwinism were discredited, as this book aims to do.
To cite more philosophy of science, the authors claim that, simply and humbly, what we are left with after dismissing adaptationism tout cur is a "whatever works" scenario (a la Feyerabend): there are many and multiple ways in which phenotypes can and do change and are transmitted across generations, and the complexity of their mutual interference and the co-evolution with the surrounding ecologies and environment makes it just too hard if possible at all to explain (which means to pre-dict instead of only post-dict) the evolution of the existent with a single theory (just like a theory of human society is practically a non sequitur). Contingency is vindicated. And this is still consistent with mechanicism, to which the authors fully abide as well as to atheism.
The authors do not veer into politics, however they ask themselves why neo-Darwinism was not abandoned just like behaviorism was (it had the same structure and faults, in their opinion). Here I cannot help but think (admittedly influenced by Enzo Pennetta's books) that the reason is that without even the semblance of an all-encompassing naturalistic theory of evolution the scientific priesthood would feel empty and ungrounded, and could not defend its status against the previous, religious priesthood - in fact, the authors admit to have been advised to avoid the controversy also for this reason, not to give such strong arguments to the "enemy" and instead keep continuing lull ourselves with a posteriori but ultimately arbitrary though plausible at best explanations of historical events.