The
overall historical narrative that he presents, about specific factors like capital punishment and infant mortality, is generally valid. But Pinker's use of historical evidence is at least as flawed as the issues with his statistics.
Better Angels literally appears to be based on a group of research assistants, without archival training, being let loose in a library and tasked with cataloguing all examples of violence and mortality throughout history.
This leads to an obvious sample bias and to Pinker basing the bulk of his argument on some truly questionable, non-peer reviewed secondary sources. It is frankly the kind of approach that would get called out if done by an undergraduate history major.
And I say that as someone who thinks Pinker is a fantastic writer, and who is sympathetic to much of the argument of Better Angels. But it's hard for me not to see some level of condescension in Pinker's approach to doing historical analysis. What he does in that book is akin to me (if you couldn't already guess, an historian) trying to write a pop linguistics book by reading a bunch of library books on the subject and chatting with the linguistics professors who have offices down the hall from me.