Sincere thanks to John Patterson for sending this link. John's wife, who's an (ex-)molecular biologist, read the JAMA paper (and the supplemental data) and wrote a long blog post about her thoughts on the genetics parts of it on the above link. He says that she wrote the piece mainlyto explain to him more about what the JAMA writers had done, and what they had and what they hadn't shown. Here's a very short extract but go to the above link to see the full post, which is excellent.
I pretty much have to take the anatomical data, and the egyptological discussion, on faith - I have insufficient knowledge in either of those fields to examine the data critically. The genetic analysis on the other hand is closer to my own field, so I can poke at it with a more professional & critical eye. Though you should bear in mind that I'm 5 years out of date and this wasn't quite my field when I was current. So before I go through the actual data, here's some thoughts on the methods/presentation.
They don't discuss the details of the extraction of the DNA from the bones of the mummies - they do however cite 4 papers (only 2 of which have overlapping authors with this paper) for the method they use, so I'm inclined to think (without reading those papers) that this is a known and tried method in the field of ancient DNA extraction.
They use commercially available kits to do the genetic fingerprinting, from a quick glance through the company's website they're used for more modern forensic applications too. I was, though, concerned that although they use 16 markers on the Y-chromosome analysis they only use 8 markers for the autosomal DNA (the rest of the DNA in the nucleus that is not sex chromosomes). The kit seemed to allow you to test more markers than that - but they don't mention why only 8. Was it that they had good data for those 8? or is this an accepted practice? (as I said, this isn't quite my field). Some note of that might have been nice.
They did analysis on 30 samples for each mummy, taken from different biopsies - it might've been nice to have seen a figure with the biopsy locations marked on it (in the supplemental data perhaps). And it would've been nice to see the numbers - the data given is noted as the "majority", but I think I would've liked to see the actual figures. It makes a difference if something came up in 16 of the samples or in 29 of the samples.
I would also have liked to see some controls! In the Y-chromosome analysis they do compare the three male mummies with another unrelated one. But in the bulk of the data they don't show the control data.