I didn't really have any intense problems with this during my first day of use. It was a little clunky to add songs to My Music and to playlists without accidentally doubling since the feedback mechanisms for showing you what's already there are very, very poor. But I managed to create playlists I liked, and it was all streaming while I was at work with no real issues.
I have an unlimited data plan, but I decided that I'd rather not use up tons of data when there's a "listen offline" option, so I tried that. Turns out these songs took up much more space on my phone than I anticipated, so I tried to remove the downloaded versions. This is where things got a little messy.
The app was very inconsistent about handling the offline versions. I found the toggle to show only offline versions, but not all the songs gave me the option to remove the download from my phone -- in most cases, I had to remove them from My Music entirely to get them off the phone. Whatever. That's inconvenient, but it's not that slow to re-add them to My Music.
I decided to clear out my downloads for some of my purchased music, too, since I don't mind listening to that at home via wifi since I've listened to most of it enough at this point. Problem is - now those purchases aren't showing up in iTunes anymore. It's as if I never purchased them.
I'm beyond livid.