I have the same problem, with duplicate (and even triplicate) e-mail recipients being listed in outlook. I have tried uninstalling and re-installing outlook connector (it must be an outlook connector problem, as the duplicates do not appear when I access my e-mail without using outlook). It didn't seem to make much difference, although the strange thing is that it doesn't happen with every incoming e-mail - some are OK, but others are duplicated.
I can't seem to find a way of bringing this to Microsoft's attention, as I can't find a "help" section in the resource centre of Office Live Small Business. Let's hope someone at Microsoft is monitoring this discussion board and posts a fix. In the meantime, if anyone has found the answer - please let us all know!