If you haven't read the paper talked about in the blog post, you should. It doesn't quite do as much as claimed (fully resolve the problems with Born probabilities in Everett quantum), but it is much more clearly argued than the usual forays into Everett (I suspect its the collaboration between the physicist and the philosopher responsible).
In particular, its the cleanest set of assumptions I've seen that lead to a nice Born rule in an Everett situation (Deutsch/Wallace was all sorts of nonsense).
Last impressive bit of progress in the QM fundamentals I recall was Zurek's einselection, where he claimed to show that only the copies of eigenstates survive decoherence. The approach was unusual enough to be taken seriously, even if the experimental confirmation leaves much to be desired. Carroll's "rational observers must believe in Born rule" looks rather dubious to me, mostly because it still takes a classical observer as a fundamental entity.
Another month, another rationality quotes thread. The rules are: