1. kill the first-load chrome download bar (I don't want it until I know I like the service) or make it non-blocking
2. use something like pushState (or location hash) to have all URLs always be referencing something useful (like the current song)
3. a canonical share source (solved by point 2) rather than *just* social-network buttons
4. add a "recently listened" thing of some sort
A few other ideas:
5. add a "listening with XXX others" count (specific to artist/track), for social proof of a different kind :)
6. add an "up next" with the option to skip
7. channel combinations (might be possible already? but the ability to listen to post-rock + ambient-electro would be cool, might confuse the UX)
8. nicer design.. it's ok at the moment but definite room for improvement.