Sean Carroll has a nice explanation of the general idea on his blog that falls somewhere between newscientist's uninformativeness and the usual layman-inaccessible arxiv article.

An interesting paper. My complaint is that they seem to be mixing multiple meanings of "decoherence," i.e. "The way that quantum interactions of big stuff get hidden in what's basically thermal noise" and "the effect that makes us measure one thing when we look at stuff."

On the macroscopic scale, they're pretty much the same, but it's still the difference between "practically always" and "for all possible configurations." Mixing these two things is what leads to the requirement of infinite entropy, actually, so I think the "multiverse" part of the interpretation is quite unlikely.

EDIT: I was too hasty. It can also be viewed as postulating that the two things are the same and then seeing what would happen, which is fine. But not, I think, necessary.

One of the references within the article there caught my eye. Max Tegmark was a coauthor. It was also the one paper that didn't have me cringing with some of the language used.

My physics and in particular my cosmology isn't at the level where I can properly evaluate the likelyhood of the model being correct. That said it has sufficient coherence that it seems at least worth keeping in mind. I've wondered for a long time what, if anything, could be underneath those equations.