I'm not quite sure how to phrase this properly, but the lack of democracy. What I mean is that democracy/politics need to be both there (which is the case with a lot of the EU) and also visible/tangible to your average citizen (which in my experience, living and working in three EU states is not at all the case). I could go on and on about how remote it seems, how even governments treat EU politics badly etc etc. Regardless the deficit is there and people don't much like it. Also add in dodging the EU constitution vote down, Greece, multiple reruns of votes in Ireland on treaties etc etc.
The EU is a horrible bureaucratic mess. I don't see much possibility of meaningful reforms, when they can't even agree not to have to move the whole HQ between Strasbourg and Brussels every month to a huge cost, to no gain.
As said, I reluctantly voted Remain but am now hoping that a Norway deal can be pulled from the fire but probably expecting some Canada style fudge.