What China has failed to do do is to bring the majority of its population along for the ride. This may not be a serious 'problem' in the short term- they can, after all, shoot, with impunity, those who do not toe the party line.
However, where in history does despotism ultimately lead to stability and ongoing financial security? Yes, China may 'dominate' the next half century, but their pre-eminence will fizzle out. It is built upon sand. Their massive population imbalance, (m/f) alone, will destabilise them.
To me, China's biggest problem lies with the fact its economy is entirely dependent on supply, not innovation. That need to supply is currently buoying up economies like Australia's (and much of Africa) but the Chinese need people with the wherewithal to buy what they're making. That won't be us, will it?
I have to say that much though I loathe the Mitt Romney-esque American (educated, at least 'middle-class', self-reliant, curious, right-wing, conservative), the fact remains, their 'can-do' (which most of the rest of us only experience during wartime) will 'inherit the Earth'.
It won't be soon, it will be ugly. But I think China's shooting star will be bright but short-lived.