I have very little with which I can disagree with in this Mark Thomas piece, To claim someone has 'Viking ancestors' is no better than astrology. His conclusion:
Exaggerated claims from the consumer ancestry industry can also undermine the results of serious research about human genetic history, which is cautiously and slowly building up a clearer picture of the human past for all of us. Many of the commercial companies plant stories in the media that sound exciting and seem scientific. But very often they are trivial or wrong, are not published in peer-reviewed scientific journals, and just serve as disguised PR for the company.
The only caveat I would offer is that the sort of confusions and misrepresentations that occur with Y and mtDNA phylogeography are dampened when you are looking at a million markers throughout the whole genome. This does not mean there are still no confusions and misrepresentations (e.g., the reference populations matter a great deal when you present someone as a linear combination of X populations, and that summary is still not reality as such, but an informative model). One alarming aspect of the trade in Y and mtDNA is that I've met several people who somehow believe that only these lineages are ancestrally informative. That is probably a function of the ease with which you can say someone is "descended from Niall of the Nine Hostages." Addendum: I actually asked Jim Wilson on Twitter if I could get a look at the raw results (not even raw data) for the claims made. One major problem when scientists have a go-to-media-first strategy is that things get out of hand very quickly.