Trans national currencies are generally a bad idea because monetary policy is one of the most powerful tools governments have to manage their economies. Central banks can set the interest rate for the region that uses a certain currency, which will either increase or decrease spending. Decreasing spending can have the effect of fighting inflation, while increasing it can decrease unemployment.
The problem is that economic conditions in certain places are different than they are in others. Conditions in Italy might call for stimulus while conditions in Holland call for a tamping down of spending. This is true of all currency unions, of course, but the analytic nationalism of our time makes it less problematic. Italy will be pissed if they're asked to endure mass unemployment so that the Dutch don't deal with inflation. Alabama, on the other hand, is probably not even aware that economic conditions are so much different in California that they require a different monetary policy.
This economic integration without political integration is ultimately the root of the eurozone crisis.
Lack of control over their own currency also leads to fear of default. A nation that borrows in their own currency can't really default, because they can print their own money. They can just print enough to meet their debt. This tends to produce a ton of inflation, which can be really disastrous if the debts are incredibly large (viz. Weimar Germany), but the worst case scenario tends to approach much sooner when you can't coin your own currency than when you can't. Greece, for example, if they could just print currency to solve their debt woes, would see a good deal of economic pain from the resultant inflation, but it would not be threatening the entire world economiy, as it is now, and they wouldn't see Weimar era levels of inflation.
