I am not an expert, but I did take a couple of semesters of history, and I find him rather annoying.

Somebody who should have been infuriated was Manuel Eisner, who wrote the paper Long-Term Historical Trends in Violent Crime. It's a really good paper, and I have seen Pinker misquote it, so he can't claim ignorance.

Eisner's argument, which I find persuasive, is that it was not the state power increase as such that decreased private violence. Because if that was the case, southern Europe wouldn't have lagged as much as it did. Rather it was the transformation of the nobility from personally very violent knights and lords, to officers and bosses who wields state violence. And that happened at different times, matching the decline in private violence. With the nobility no longer needing personal violence, it goes down. Quite different from Pinker's take.

And then there is the question of where that state capacity for violence was wielded. I don't think Pinker includes Queen Victoria in his rouge gallery, yet the famines in India killed about as many as the ones in the Soviet Union and Communist China, and those are usually counted as state violence.

On the rise and fall of violent crime in the west during the 70ies and 80ies, there has been many candidates, but most fall away because they can't explain it both in western Europe and the US. One good candidate is leaded gasoline leading to lead poisoned babies growing up and becoming more violent in the crucial young adult age. It matches, but I haven't seen any proper attempts to really test it, by for example comparing cities to the countryside.