"This rather fanciful interpretation of Quantum Physics has now become accepted by many theoretical physicists as being more satisfactory than the Copenhagen interpretation, despite the fact that the mechanism which causes the splitting of the Universe is not explained in any more detail than wavefunction collapse. As you can probably tell, I am in the minority of physicists who finds the Many Worlds interpretation dificult to accept, and not particularly illuminating."

I think these lectures are a good intro to QM. This statement feels very emotional though. Many-worlds just states there is no such thing as wave function collapse. The many worlds are a logical conclusion following. Copenhagen simply refuses to elaborate to when wave-function collapse happens, which to me is not a complete theory.

You could have some critique of many-worlds in relation to statistics, although I think many people have given quite satisfactory explanations.

Many worlds is just bare bones QM.. If any other theory is proposed, it should be falsifiable (like pilot wave theory for example). Doesn't mean it won't be difficult to measure.