Much of what was mentioned in the program would not be new to readers of this blog. A couple of things that stood out for me was the demonstration of "Neanderthal pyrotechnics" by Wil Roebroeks. Related articles:
Meyer et al. (2012), according to which:
We estimate that the proportion of Neandertal ancestry in Europe is 24% lower than in eastern Asia and South America (95% C.I. 12-36%).It will be interesting to see Dr. Hawks's study when it is published. But, it seems to me that there might not be a real difference between the Hawks and Meyer et al. findings, because the former seem to be counting shared derived alleles, and Europeans would have more of those than East Asians, simply because they are more heterozygous across the genome, and Italians more than Britons. An ASHG 2012 abstract also seems to find more Neandertal-derived alleles in Europeans than in East Asians. So, it might seem that Europeans have inherited a more varied set of "stuff" from Neandertals, but East Asians inherited a larger portion of their ancestry from Neandertals overall.
On the topic of documentaries, I found the recent Prehistoric Autopsy to be extremely good, and you can probably find it fairly easily online if you don't happen to live in the UK.