There are several problems.
First and most recent, we had the stupidity to make a common currency without having a common ministry of finances or even common tax policies. Instead, the countries are competitors, all trying to attract investors. The smaller countries bankruptcies are almost 100% due to finance market g@mbling and negative rating agencies assessment of state papers. That has nothing to do with real, productive economy. It's all speculators money that's going up in smoke. The large Banks of the world have been playing C@sino-Europe, giving large capital investments into tiny countries and hoping for fat interest rates. It was all a mighty bubbly foam. And the bubbles are now bursting, one by one.
The other thing is the epic democracy-fail. The European Union leadership is a group of representatives who represent the different groups of representatives that the people of our countries elected. It's an indirect, indirect democracy. There is of course also a European parliament directly elected by the people. But they have hardly any say in anything.
I get a bad feeling, that every lobby of industry has more say in European politics than the citizens of Europe. We have hardly any All-European political parties either. Only the green parties of Europe and the pirate parties of Europe managed to have international organization at all. All the parties that make big fractions in their own countries have no networking with other European countries political parties. It's all chaos.
For me, the only way to make this mess really work would be to consolidate all countries and make a real, democratic, new constitution from scratch. With the European nations being something like federal states. A single government elected democratically by all people of Europe. And just dump the old borders and all the nationalism. There's no big difference really between a German, a French, an Italian and a Greek. We have different languages, but that other than that we're close.
Biggest would have to be Greece leaving and Germany bailing them out of it. Also a problem is that Germany is by far the strongest country in it. [Deutschland!]
Smaller counties going bankrupt, and the real possiblity of that union breaking up soon.
France is about equal.