From my experience I think it has to do with the library not being synchronize to the phone yet.
It played fine on your Vibrant because it was synced to it, now that you got a new phone it needs to sync in it's entirely in order to play continuously.
On my phone (not a SGS2, yet) it does the same thing, but I'm constantly switching roms so it never gets to completely synchronize.
I would say just give it some time and it will eventually all sync.
It helps if you got it connected to wifi. Less buffering.
Not sure if changing any settings can help other than going to the app and selecting the option to hide unavailable music.