The "resuming" thing is interesting. I actually wish that IE would resume, or at least give me some indication that it is still processing the page. But the only real issue I have with Windows Phone is that email does not automatically save drafts. I've lost a lot of good work this way.
Music app could be better, but I've pretty much figured it out. I still think that the Music app should automatically cache music while playing. I just set up playlists and set those playlists to work offline it is much easier that way. Even better if you do it from music.xbox.com as opposed to the actual app.
This may not be a Windows Phone thing, but I would like music.xbox.com to give me the ability to automatically save playlists offline from there, so I don't have to individually go into each playlist on my phone and set it up. This may be a lot to ask.