Normally the "who watches the watchers problem" is handled via a separation of powers. I don't know much about the EU government. Does anyone know if they do this?
Yes. The European Court of Justice is independent from the political and executive structures (and gives them a fair number of bloody noses, too). But the ECJ cannot prosecute anyone if the rules are nebulous and still somewhat in flux - as they often are, because a lot of EU institutions are extremely new in historical terms.
What is required, at the moment, is strong political oversight, particularly from the media. Light is the best disinfectant.