So already some initial thoughts after using Spotify for an hour or so... I've used Rdio extensively as well as MOG and still do use locker-based services like Google Music and Amazon Cloud.

- Why isn't there a WebApp (unless I'm missing something) -- this is a no brainer
- I really am impressed by the bootstrap time on songs compared to nearly all the other services, even over 3G (EVDO in my case) songs start up almost immediately. I believe this is because they do more tricks with caching and p2p access to stuff.
- Spotify is really great if you know exactly what you want to listen to. Rdio seems superior for music discovery.
- The desktop app in particular is fantastic, a little too iTunes-ish for my liking but extremely functional and better than any other offering I've seen.

Android-app specific (I haven't played with the iOS version just yet but they are extremely similar)

- The equivalent of a "Collection" on Rdio is the Library feature on Spotify which is nice but I'd like to be able to filter this in a more meaningful way given it's going to be (for most people) their largest list of stuff. Not being able to view this by artist is extremely annoying. Unless I'm missing something, when this list reaches even a few hundred songs (I had thousands over on Rdio) finding something you want is pretty fruitless (especially an album) unless you actually use the search function and type it in.
- Everything is very playlist/track centric, which actually may work well for a lot of folks but I really consume music in a more album-centric way which the current UX on mobile doesn't really cater to.
- The app really needs a Home button instead of relying on the user repeatedly hitting back to go back.

Regardless, the thing that's going to be killer for Spotify is the fact that they have a free offering -- it worked in Europe, and no doubt it's going to be huge here. They are going to have to rework their social strategy a little (beyond just linking to Facebook for sharing), but I don't think that's going to slow them down just yet.
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