A very useful feature to me would be to be able to pause the internal player by right-clicking the tray icon, and unpausing it again by the same means.
A little more on the speculative side, double-right-click opens a menu with the above feature, and probably an 'Exit' option for now. I think the menu could look like this:
I guess you wouldn't need 'Play' and could simply change 'Pause' into an 'UnPause' option when the stream is paused.
The menu could allow for other configuration options, but I think the simple, pause on right-click wouldn't be all that hard to implement, and more useful. I may be wrong though