Does every event with two possible/plausible outcomes result in two distinct worlds? I don't _think_ that's the case -- it seems that multiple plausible outcomes also result from an ambiguous problem description (even if the situation is actually completely deterministic).

If the exact physical state is underdetermined by the problem description, then there will be separate branches of the wavefunction for each possible state, although they might have diverged arbitrarily long ago. So, yes.