In fact there are many continuous outcomes in quantum mechanics. The overved velocity or momentum of an electron or any other mass. In fact the number of stated problems where the results are broken down in to discrete states is small compared to the ones with continua. In fact, the heisenberg cat example, there are not just two states of outcome, either alive or dead. Rather there are a myriad of state outcomes where the cat is alive, and another myriad of outcomes where the cat is dead.

I personally think the many worlds hypothesis is ludicrous, failing Occams Razor by such an astonishing margin that it might as well just grow a long beard. Admittedly, I have not read any respected physicists argument for it (or at least I didn't respect the arguments I did already read). I think the many worlds hypothesis is just a very dopey hack for people who have decided ahead of time that the universe "just HAS to be" deterministic. I say if you observe indeterminism in the universe, then it is your theory that is broken, not the universe.