Steven is basically right about my views. Though the criticism of vagueness only matters so long as people insist on being vague. In principle there could be a functionalism in which the functional states are microphysically distinct natural kinds, and a many-worlds interpretation in which the worlds are exactly individuated and enumerated. But it's not an accident that functionalism and MWI try to tolerate vagueness; it arises naturally, given the theoretical entities which are asked to play the role of "mind" and "world".

Po'mi could ask Ha'ro, "How thin is thin enough?" (to fall apart). That's the counterpart, in the story, of the decoherence threshold that remains unspecified in mangled-worlds theory. As an exercise in saving the phenomena (in this case, the observed relative frequencies of experimental outcomes), it is fair enough to say "if it happens somewhere in this range, the numbers work". But the theory would still be incomplete, for the reasons Po'mi raises in part one.