United currencies work best in transfer unions: that is, political entities in which it is acceptable (on the balance) to residents of one region that their tax dollars be siphoned (in part) to service other regions of the union. The United States is an example of such a transfer union. So is the United Kingdom: Liverpool may be performing shoddily and require funds from London to keep the schools open and the roads safe, but nobody complains much. This bargain is palatable (in part) because of the sense of shared sacrifice, common cause, and collective governance.
This is NOT the case in Europe. Germany is not pleased about paying Greece's public-sector debts because (in part) they feel they have no say in how Greece has spent its money. When the wealthier parts of Europe try to construct a debt-relief plan it includes heavy austerity measures because the banks (and the populace) in these wealthy parts feel they aren't running some charity; the Greeks resent it because they feel put upon by foreigners. Thus the Eurozone is being smashed against the reality of insufficient common purpose- common sovereignty, common tax-raising authority, common finance and spending policies.
It's reasonable to expect, I think, much the same would happen with a single world currency. There must be a counterflow to the flight of capital and the loss of demand; transfer unions are one way for that to happen and not bloody likely in a worldwide currency regime. The other best option is currency revaluation.