I would add another point with regard to observer-moments and continuity: probably there is no unique "next" or "previous" relationship among observer-moments.
The case of non-unique "next" observer-moments is uncontroversial, as it relates to the universe splitting predicted by the MWI or the analogous effect in more general multiverse theories. Non-unique "previous" observer-moments can probably happen as well due to the finite precision of memory. Any time information is forgotten we would have mental states merge. This requires a general multiverse theory, or at least a model of mental states that span MWI branches; the conventional MWI does not merge branches which have diverged through irreversible measurements. In this view, then, we can chain observer-moments together to form observer-paths, or more simply, observers. But the chains are non-unique; obervers can intersect (share observer-moments and then diverge), or even braid together in interesting ways. That means that there is no unique sense in which you are a particular observer, at any moment; rather, you can be thought of as any of the observers who share your current observer-moment. Hal Finney