There are two arguments that are presented in both of these comments. The first is that the historic and pre-historic data on violence is incomplete. For this, there is no doubt and Pinker spends a lot of time talking about this. This is true for a vast majority of topics and its unfortunate that there is just a whole host of things we will never be sure about due to the non-existence of preserved evidence.

The second takes issue with his use of per-capita comparisons and suggests that an absolute rate may be a better measure. This is extremely silly and Pinker spends very little time discussing it because it really is absurd to entertain. For one, it implies the only true solution to any violence is massive population control. And two, it negates any comparison to cultural or behavioral change by simply pointing to the population size of the planet. Think of the statement, "Modern medicine has not advanced from the hunter gather days because more people under the age of 40 die every year than did 5000 years ago."

Edit: The second comment brings up a third point that the lower rate of violence does not imply we are better off, and is therefore questioning what we should define as violence. Pinker again readily addresses this issue by explicitly defining the type of violence he is analyzing, physical, and repeatedly stating that these issues are outside the scope of his book.