One of the biggest problems with the European Union is the "democratic deficit". While there is an elected European Parliament, it cannot initiate legislation. Instead, that function is performed by the European Commission, the "executive" of the EU analagous to the NZ Cabinet. Unlike the Parliament, the Commission is not elected, but appointed by the member-states, and is frequently used as a sinecure for retired or has-been politicians. The result is a lack of legitimacy and accountability; the Commissioners are not generally accountable to those in whose name they govern (they are not really accountable to Parliament, and are forbidden from taking direction from their national governments).
Last year saw the first stirrings towards correcting this, with the European Parliament leveraging its power to approve the entire Commission into a veto on individual Commissioners. Now, one of the diaries on European Tribune is proposing the next step: taking the choice of the President away from the (again, unelected) Council of Ministers and making them subject to the Parliament. The mechanism for this is simple: the President must be approved by the Parliament, so one of the Pan-European political parties or party groups should simply choose a candidate of their own, and threaten to veto anybody else. They would of course require a majority, which in practice would mean gaining the support of other party groups - but that is no more difficult than the appointment of a Prime Minister in many countries. The joy of the proposal is that even if it does not work, it will encourage the other parties to do the same thing, and help build a truly European political culture, rather than one which is mostly about national issues on a larger stage.
The EU isn't yet a super-national government, and despite the commitment of its individual member-states to democracy, it is not yet democratic. But the potential is there, and given time (and a few ambitious politicians) I have no doubt that it will be fulfilled.