The wavefunction is a superposition of n independent wavefunctions at different amplitudes, like you can divide a piano's sound into a bunch of pure sine waves. "From the inside" each feels like a self-contained world (in a physically rigorous sense), but the ratio between their amplitudes and phases can be an arbitrary complex number - just as even if you're only playing a C and a G, the ratio of their amplitudes can be anything.

Why is this a problem? This complaint looks to me much like someone complaining about the Pythagorean theorem because it results in irrational numbers. (And yes, historically there were such complaints. And no, that is not a good reason to discard that theorem.)

A system described by physics evolves according to the laws of physics. We find the result surprising. But that is because we have bad intuition, not because physics is fundamentally broken.

> when collapsing superposition of two states you might need to (or rather almost always) need the ratio of worlds with outcome A to worlds with outcome B to be irrational. So unless you create a continuum of new worlds each time it won't work.

Has this been shown? I would want any such proof inspected for hidden continuum assumptions existing in the probability calculations, thus leading to irrational probabilities.

Try reading http://arxiv.org/pdf/0903.2211.pdf This basically presents many worlds as a mass density obtained by integrating out the wave function. The worlds we see can be traced through the evolution, like two videos overlain on each other can be deduced over time.

The Everett Interpretation is best thought of as the idea that collapse just doesn't happen. Which means that there aren't discrete integer worlds but only higher and lower amplitudes. If you had discrete worlds that would also be a problem because you could change how many worlds you had by how you did the math.