"The issue is that violence is a poor metric for progress." Just to echo the commenter, I don't think Pinker is stating that humans are progressing in general - he is just stating that violence is decreasing. I also agree this is a measurable metric, that Pinker does well to argue for.

If he claims things "are getting better", I think he says that "violence is decreasing", where "violence" is a measure of worseness.

If we want to talk about progress, though, we would have to define what progress really means. Will Durant (from "The Lessons of History") says progress is more like the increasing ability of mankind to control his environment. If so, I would think there is some evidence for that.

In terms of social injustice, Will Durant also makes an argument that there will always be this. Power is always concentrated to the few (that's just how it works in order to have organization), and those not in power will always have some level of injustice. The amount of people in power and their motives can change depending on the era/civilization/society.