My primary concern with the European Union is as follows, so please do correct me if I'm wrong!
The UK is governed by the largest block of elected MPs that can agree to work together. The Government then acts as it sees fit yet is constrained by all the elected MPs=Parliament (and the House of Lords) on certain matters. The Government has the power to do other things without reference to Parliament.
The EU is governed by the European Commission, acting as it sees fit, yet is constrained by all the elected MEPs=European Parliament (and the Council of European Union/Ministers) on certain matters. The European Commission has the power to do other things without reference to the European Parliament.
(Confusingly the BBC seem to be referring to the European Commission as equal to our civil service - although the Commission has civil servants, it appears to also include functions like our government ministers.)
The Commission isn't directly elected, and the Commissioners must not represent their own country. The President is elected by MEPs, then the remaining commissioners are appointed by the Council (ministers of national governments), and accepted or rejected as a block by the MEPs. Similarly, the Commission can only be removed from office as a block (by MEPs).
So, unlike the UK, the EU Government isn't directly elected, and can't be removed from office by the citizens.
It's probably a matter of faith (as chdot notes), but wouldn't it be better to have a more democratic system of government?
(Acknowledging, of course, that the UK Government is only a little more democratic being majority rule, and having an unelected upper house.)
To be honest, this point doesn't seem to be being considered much in the rhetoric, so perhaps this is too subtle to matter?
Robert