The EU Council has adopted the Software Patents directive unanimously, despite the fact four of its members opposed it.
To many Europeans with an interest in software freedom, this issue has been their first encounter with the mechanisms of the EU. They might easily assume such anti-democratic manoevering is exceptional. It isn't. It's business as usual. What the politicians at the heart of the EU want, they get, and the rules don't matter.
The EU's annual accounts have not been audited -- for ten years running
Denmark voted against the Maastricht Treaty in a referendum in 1992. A small change was made and they were asked to vote again. If it was the same treaty, they had already rejected it. If it was different, all the other signatories needed to ratify the new one. Never mind.
The stability and growth pact was agreed before the single currency was introduced, limiting members' fiscal deficits. Several member states have exceeded the deficits, and the pact has not been enforced.
Whenever a new Treaty is introduced, we are always told that if we reject it we will lose all the (alleged) benefits of EU membership, despite the fact that everyone has committed to the previous treaties, which logically would remain in force. The implication is that prior agreements are worthless. (example: see the very end of this piece from "Britain in Europe").
That's just off the top of my head. (now updated with references: I don't demand anyone take my word for this stuff).