Hi there, I'm having the same problem.
Hero was fine until I did a factory reset (I'd cleverly managed to lock myself out of it via the security swipe).
Anyway, did the factory reset and now I get the android.process.acore has stopped unexpectedly problem.
I'm not that keen on installing other ROMs at this point, just hoping you can share your solution.
I'm guessing but it seems to be connected to my contact card within contacts. (If i wipe the info in that and log out of facebook the issue stops).