Update 2/16: Can't reproduce this problem anymore; seems to be fixed now.
I can't log in to the web player. I have been having this issue since 2/09, and maybe earlier. I have a premium account and I use Facebook to log in. When I click the "Log in" button, I get an error dialog stating "Login Error: There is an error in logging you into this application. Please try again later." (See attached screenshot) It looks like a Facebook integration error, possibly.
I have tried logging in using Chrome on Mac, Chrome on Linux, and Firefox on Linux, all with the same error. The only way I was finally able to log in to web was to go to the desktop Spotify app and open Spotify Community from there. Unfortunately I cannot install the desktop app on all the computers that I use, so I hope this issue can be fixed.