I just tried it in both Safari and Firefox (latest versions) on a Mac and it does still have problems playing the next song if the tab it is in is not active. As soon as I tab back to SilverPlay it starts playing.
My outgoing network speed shouldn’t be a problem. The Firefly server that I’m streaming from is on a high speed university server. I am offsite, with Silverplay installed locally to my machine. I’ll try installing the client on a machine that is on the same network tomorrow and see if it has any effect.
The Silverlight platform is pretty new, so it doesn’t surprise me that there are hiccups, but what I’ve seen I like so far.