This was an ok book that had some interesting facts, mixed with kind of obvious scientific findings, and a few questionable studies. The author seems somehow a bit naive, and sticks to research and lines of thinking that match his hypotheses and world view, and doesn't spend any time on counter examples or more exceptional situations. Therefore if you read the book uncritically, it's a wonderful explanation and everything makes sense; but if you stop and think about it, you can often find counter examples that make you wonder how generalizeable his explanations are.
The novel idea that the author introduces is pretty neat; that "beautiful" traits can evolve not because they serve a purpose, but because they tap into a pre-existing preference the choosing mate has. Recurring examples of this are preferences for the color of foods (e.g. reds) or symmetry. While these can often also be a marker of good health, the specific form they take in every species varies according to these "hidden preferences" that are not specifically beneficial. A nice example of this is in 2 species of closely related fish, one with ornamental tails, the other without; when scientists added tail ornaments to the species without, those fish were preferred by their own females, thus demonstrating that the preference was already in place, and all it took was the sudden appearance of tail mutations to change the trajectory of the other species.
The book gets into various details on different mechanisms that further push and pull these evolved traits designed towards sexual attraction, such as the obvious trade-off between catching a potential mate's attention and a predator's attention, to the less obvious impact of Weber's law putting a cap on how extreme a trait can evolve.
The main problem with the book was the author's rather naive view of beauty, sexual attraction and evolution. Throughout the book, he never makes the distinction between "beautiful" and "sexually stimulating", basically implying that animals always see each other and various sexual traits as "beautiful". While there's no reason to believe animals can't appreciate beauty, it's obvious from our own experience that not all beautiful things are sexually attractive, and not all sexually attractive things are beautiful. This is obvious when considering a gay man and a straight man, both of which would say the same woman is beautiful, but only one would actually be sexually attracted to her. Vice versa, male genitals are rarely considered "beautiful" by women, just sexually interesting. So if a female frog prefers to mate with a male frog that makes "chuck" sounds, it could be that it appeals to the lady's aesthetics, but it could also just be pushing the right sex buttons in her brain. The distinction between aesthetic beauty and sexual attraction is not usually terribly important, it just gives this veneer of 18th century romanticism to animal sex lives.
This sort of smoothing over the details of attraction and beauty becomes a problem when the author starts speculating. In particular, he introduces the concept of MHC genes. The idea is roughly that MHC produces slight changes in animals' (and humans in particular) odors, allowing individuals to identify conspecifics who are genetically different than themselves, making them a good mate. It was sort of found (but there are some counter studies) that women prefer the odors of men with different MHC genes from themselves, but when on contraception preferred men with similar MHC genes. The author speculates this may be because contraceptives "trick" the brain into believing the body is pregnant, and so the woman is better off looking for family to help raise the child rather than genetically diverse mates. Extending the argument to the next level, a couple who meet and fall in love while the woman is on contraceptives might suddenly find her partner unappealing and too much like family when she goes off the pill. Ignoring the possibility that the studies could be flawed (such as failing to account for correlated variables), what's really wrong with this line of reasoning is that it is essentially implying that evolution would make pregnant women sexually attracted to family members! This would not have happened if the author had in his mind the actual distinction between sexual attraction, and just attraction.
Lastly, the author occasionally slips, and falls for the fallacy of viewing evolution as being by design, with a purpose. This occurs multiple times, but two telling quotes are: "what we do not see are the graveyard of [evolution's] attempts to be beautiful" (there are no attempts, only accidents that prove useful to the individual, and later species) and "Amazon mollies resulted from an evolutionary mistake" (all genetic changes are "mistakes"; if anything, a mistake that manages to lead to a successful species wasn't much of a mistake after all).
This is not just about nit picking; having this flawed understanding of evolution will mean misinterpreting the data and trying to push for hypotheses based on purpose, asking baseless questions like "why did this evolve?" rather than "how did this evolve?"