In general, there is no good concept of a music collection (despite the UI having words "Collection" and "Library" in it). While you don't own albums in Spotify, I still sorely miss that concept. Starring entire albums makes for a fairly useless/unwieldy Starred playlist, so that's a no go. I've resorted to starring single songs, then later selecting a song from the starred list and then switching to playing the whole album (if I starred the first track of the album, I have to select another album track, then back to first track, to make it play the album and not just continue on the Starred playlist).
Basically, where's my damn list of Artists and Albums I've liked? In iTunes (or mp3 folders back in the day), I would scan the list of artists and select an album to play.
No, I do not want to have an all songs/genre playlist and then sort by artist and then page thru pages of tracks.
The mobile app has poor information architecture. Going back to the starred playlist (or any other playlist) takes 6 taps if I'm on the info screen.
Oh, I freaking hate the mobile info screen. To me, it always feels awkward to hit the song name at the bottom to bring up the "now playing" screen, then tapping "i" to show the info screen, just to select the album or the artist of the song I'm listening to. As far as I can tell, the whole point of the "i" button is to allow me to see the album art--but, bizarrely, seeing album art is the default (so always requires an extra tap to do anything related to artist or album).
Basically, it's a damn tapfest. It's frustrating when you want to switch songs or do some navigation quickly--for example, while in the gym on an elliptical or while running.
Also, there is no search history and the app is forgetful. Periodically, at unknown intervals, the mobile app forgets the album/song I was playing, and I have to re-enter a long artist name all over again. Not to mention there is no fuzzy search. Yeah, try spelling "Irresistible Force" correctly, quickly.
There are the things that make Spotify merely a very convenient music discovery service, as opposed to a complete, fulfilling replacement to owning your own music library.
Finally, there is general bugs, like crashing and streaming getting stuck now and again, which can be very frustrating in the middle of an album (the next song streams, this song is stuck).