MW does have at least one specific problem: there is no easy way to account for the specific probabilities in quantum experiments. If an experiment has two branches, and the reason for the probability is indexical uncertainty, then each branch should have a probability of 50%, while in fact this is not necessarily the case.

Robin Hanson has suggested an answer to this with his "Mangled Worlds" interpretation, but this answer has yet to be confirmed. It seems to me that Eliezer as usual is overconfident: MW might very well be true, but it is nowhere near as certain as he suggests.