Specifically - the bass issue a lot of people have noted. It isn't the bass impact that's my problem, but rather there seems to be a limited frequency range that's just way too present, think bass guitar notes. It's bad enough in my opinion that it makes the music it happens in unpleasant to listen to, and with headphones >= $200 I don't feel I should have to compromise. I slapped in a little bit of dynamat, and that definitely helped, but didn't totally fix it. In fact it seemed to narrow the frequency range, but when it DID hit it, oh boy was it resonant and ugly.
Beyond that - I like a little more midrange presence. That comment on the AH-D340s caught my attention. I'm just worried about comfort, since I've yet to have a pair of on-ears that didn't hurt after about a half-hour.