Sharing playlists, chatting in the messages, and finding users should be much easier for people that do not have a Facebook Account.
For example, if the user does not have a Facebook account the friends tab is useless. You should be able to have "Friends" without Facebook. There should be a "Friend" button and a "Follow" button when viewing a Spotify user.
I suggest creating these tabs (feel free to critique): 1. Friends - You friend people by clicking the "Friend Request" (or similar) button on a spotify user's page. You could also show suggested friends pulled from the users Facebook friends (and friends of friends) that are using Spotify, and you could add a "Email" button for friends that are not on Spotify yet.
2. Following - These are the People, Bands, and Playlists that you follow by clicking the "Follow" button
3. Users/Playlists (something along the lines of "Popular Users And Playlists") - This shows the most popular Bands and Users with the most followers. Secondly, you could include something like "Most Popular Playlists" or playlists that have the most followers.
Lastly, I think finding users on Spotify that don't have Facebook should be much easier. In order for someone to find me they have to type "spotify:user:username". There should be somewhere where you can search for users and follow them. I encourage finding new ways and possibilities to knot this together. I think the "social+music" thing to Spotify could really be enhances here. It would help to bring many more new users to Spotify and make it a much more enjoyable experience.
PS It would be really cool if people could add names and pictures to their profiles even if they don't have Facebook! Thanks!