The songs' info (album / year / artwork / etc) should always display the first / original album from which it came out, not re-releases, compilations and what not. (I red that Spotify is already working on this but I just felt like reiterating. It's really significant.)
You managed to squeeze the album name in the android widget (4x1) but not in the full player? Same for pc app... Title, artist, album and year should always be displayed... maybe except for the small widgets.
When I click on a song that's already playing, don't restart it over. Just open the artwork and info.
Spotify icon in the top corner isn't necessary. I'm usually aware that my music is playing.
Maybe not everybody will agree with me and if it's the case, Spotify should make customizable display options.