For example, in the first link the author summarizes his long comment: " In short, he's extremely sloppy with his numbers and relies on almost no scholarly sources. I would not accept the type of work he puts in from an undergraduate.". So maybe Pinker does jump to conclusions that not necessary result from the data.
The third point , about how do we define violence is crucially important. I wonder if you counted the homicide rate in nazi germany before wwii or in soviet russia after wwii , you've get much lower numbers than pre-history(per capita). But it's hard to tell with a strait face those are "better" or less violent than pre history.
Is he forgetting that Pinker writes mass-market books, not journal articles?