I have also upgraded to 5.1 and have not noticed any improvement. In playlist mode the app is totally unusable. I can tap on a playlist ten times without any response. I can swipe for half a minute without any reaction. If I then quit the app and start it again it crashes immediately. It has had this behavior in version 5.0 and 5.01, and nothing has changed in 5.1.
I suppose this is an issue with one of my playlists. I have one with with 6000 songs. A few months ago I managed to delete it on my iPad (it took about five minutes before I could even click the "cross" icon), and discovered that it had disappeared on iTunes as well. After that responsiveness was a bit better, but still a disgrace. But I want that playlist on my Mac, and so I put it back.
I don't want to have to think about this. My entire music library fits on my iPad, that's why I bought a 64Gb model. And so I want to sync the entire music library. I also don't want to check if some of my artwork is to large. If the app cannot handle large playlists or artwork, it should deal with it itself (omit that playlist, or reduce the artwork). The previous app could handle all of this perfectly, so how can the new one be such a total disaster.
It is totally unbelievable that this has not been fixed. I have no app on my iPad that is as bad as this one.
Of course I am going to send feedback to Apple once again. But if 5.1 (after waiting half a year) did not fix it, I am not optimistic. And I have not even mentioned the unattractive look and the absence of lyrics.