One thing I would say is more of a recommend rather than a "like" or "dislike" is that you really need to read at least one adventure ahead of the part you are currently playing or it becomes increasingly difficult to keep the metaplot relevant.
I would echo most of what has been said here so far:
I used a slightly modified version of the "magic item economy" since I found the current incarnation frustrating (and I agree that kingdom building gets too paperwork heavy).
I am also using the old Birthright Mass Combat rules rather than the ones presented in the AP. I just didn't like em. Honestly, I think I was more frustrated with the idea that your army just "poof" is there when you need it -- but is also ridiculously expensive to maintain... We were six years in by the time we got to part 5. We didn't have any kind of army before that? Then why do we have a General on the Court?
Most important though, I would echo the comment about the side quests. Probably the most frustrating part of reading each adventure would have to be the inside covers... "Oh, hey, you guys are high-level adventurers and the rulers of a nation. Could you go retrieve me a roc egg or a wild horse? That would be awesome."
Linked to that would be a little frustration with the way encounters were distributed. My players skipped large parts of the wilderness exploration once they were into the 3rd and 4th parts of the AP -- they were too busy, you know, with ruling their country and trying to solve the problems of their neighbors -- who were disasters apparently.
Don't get me wrong. I'm enjoying the AP and so are my players -- but some elements don't really seem fully thought out. I've considered running it again for another group and I know that it would be much improved the second time through -- so that I could have more things kept in mind the whole way through.