Besides the bugs that will eventually (hopefully) be fixed, what I find most frustrating about iOS7 is Music.
There are NO sub-menus for albums when I am browsing by artist. If I select one artist, it goes to all their songs. If I choose one song from one album, the play queue exists only within that album, which means you can't shuffle all of 1 artists' songs if you wished to do so. It's counter intuitive that it only shows discography yet doesn't let you shuffle/queue the whole discography. This also happens when you browse by genre then select an artist - no further sub-menus beyond that point.
The feature of loading every single album art is a huge pain because it makes it harder to navigate through the library. I'd expect an option to turn it on/off or something because I know some people love organizing album art. Also the phone attempts to sync artist pictures into the album art slots when browsing by artists, and it doesn't quite make sense to me why this feature exists.
I realize you can toggle which apps use Data by going to Settings > Cellular, but allowing an app to use data is the default option. If you toggle data off for one app, there will be constant notifications asking you if you want to toggle it on. I have found this particularly annoying when using Music because radio and album art syncs require data.
I apologize if someone else already mentioned these issues. I did a quick search before posting.