The Puppeteers' intelligence seems like an evolutionary implausibility, as they're derived from herbivores which are generally not very smart (because it's easy to out-think a lettuce). Then we find out that they breed by injecting gametes into the body of another species, and their sapience makes more sense: they don't need to outsmart prey to eat, but they do need to outsmart a host "female" in order to breed.
Also, as Louis Wu points out, herbivores do need brains to cope with predators. Which the Puppeteers did very efficiently, by exterminating them.
In "The Warriors", the kzinti are baffled that a human ship has no weapons. The telepath reports "Not even knives," then immediately corrects himself: the humans have cooking knives, but that's all they're used for. That should have tipped off Captain that when the telepath scanned for "weapons", he was searching for things that the human crew thought of as weapons (and getting nothing)—but if he scanned for particular dangerous items that could be repurposed as weapons (like cooking knives, or humans' primitive reaction drive), he might find something worth knowing about.
The notion that all the world's nations would pass laws mandating that criminals, even petty ones, be broken down for spare parts. Not only does this presuppose that humans have perfect faith that their legal system doesn't make mistakes, but it assumes everyone who voted in support of such a policy considers it more likely that they, personally, will one day require a judicially-obtained organ transplant — a hypothetical scenario that most wouldn't expect to arise for decades, if ever — than that they'll ever get busted for traffic violations: something they've probably committed, and been ticketed for, themselves.
It's more of an examination of Humans Are Bastards / Democracy Is Bad; no different from taxation. Lots of people complain about taxes but few want to do without welfare, subsidies, public utilities... Is there really any difference between, "The three of us are poor and Jack is rich: Let's divvy up Jack's wallet" and "The three of us are sick and Jack is healthy: Let's divvy up Jack's organs"? Especially since in Niven's universe, laser-eye surgery was never invented because of eye transplants. On Plateau, where the ruling Crew class lets a certain number of Colonist class rebels survive to continuously recruit others, Crew regularly get scalp and teeth transplants!
Setting aside all the Art Major Biology behind the Pak life cycle, one huge problem with Protectors is that Pak of different bloodlines seem completely oblivious to the possibility that they could form permanent, stable, treachery-free alliances with each other, simply by letting their descendants mate with one another. Pak breeders aren't asexual, and their bloodlines would need to cross periodically to avert inbreeding depletion anyway, so simply interbreeding two rival Protectors' bloodlines could convert them from archenemies to unshakable allies the instant they got a whiff of their first out-crossed infant. No need to wipe out each others' young, just make sure their next generation of protect-ees are your young also.
This is addressed in passing in one of the Fleet of Worlds books: Even in the Pak breeder stage, the sense of smell connection is strong enough to be able to tell family from not. It seems unlikely that the breeders could be MADE to interbreed, even if the Protectors tried.
Except that we know from Rishathra that Pak descended species will choose to interbreed if left alone.