These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: The Neanderthal Parallax
Mary Suetopia: The Neanderthal world has very little crime, hasn't had a war in hundreds of years, and lives in harmony with nature.
Deconstructed in later books. The Neanderthal society deliberately chose to breed violence out of its population because due to the size and strength of an average individual, a minor dispute could easily end with someone getting killed. One such scene is depicted in the first book; a dispute that two characters escalates into one having his mandible essentially destroyed with one punch-it's later stated that most past assassinations consisted of someone simply walking up to the target and caving their head in by their fists alone. The problem arose when they started sterilizing anyone sharing half or more of the violent person's genome as well. It's implied that the sterilization policy has actually created a pretty significant problem with domestic violence, since the victim can't report the crime without condemning any children they might have to the same fate as the abuser.
Sawyer has argued both in other novels and Real Life for something like the surveillance system of the series, feeling privacy is not only overrated but dangerous, and increasingly disappearing anyway.