Go to https://play.spotify.com/ and log in with a Spotify account. You should see the web player with all the controls to play music, browse it, manage playlists, etc. However only the Spotify icon on the upper left corner appears. Reproduced with the MiniBrowser and Epiphany 3.12.1, using WebKitGTK+ 2.4.5. My version of the Flash player is 11.2 r202. This used to work at some point, but it's been broken for several months now.
It also doesn't work with wk 2.6.0.
Looks like wiping out the localdb fixed this problem.