A world currency is based on the idea that a single currency would work. The most reccent attempt at a supra national, single currency is the Euro. It doesn't work
I'll toss out a few reasons for the difficulties associated with the Euro. The one size fits nobody monetary policy. Risk of localised hyper inflation, especially in the smaller countries. The risk of Eurozone deflation.
Tied in with the Euro is the GSP, which relaets to fiscla policy. The Euro is a tool used in monetary policy implementation, while the GSP is the fiscal policy equivilent. Flaws? yeah... the three percent limit on the general govt deficit as a percentage of GDP, in expansionary fiscal policiy, except in cases of extreme recession. The lack of local flexibility in a centrally governed system... Need I go on?
It's also fair to say that many people would not want to give up their local currency. Italy, for instance, showed intense, and sustained resistence to the Euro. Denmark refused to enter, while the Govt managed to push through membership of ERM 2. Sweden said 'No to the Euro'. Britain may never enter.
The Euro is a flawed currency, and if it's the rationale for a single currency, then the future of that currency doesn't look too good.