I'm still using the Azureus flavor of VUZE but I think this would still apply...
It's been working for me quite well these past few years with the following ports directed to the torrent machine:
39286
13818
10739
When I first set the program up - I found those ports through various web postings.
In addition, some other bit torrent ports that are opened for bit torrent (although I don't know if these help Azureus/VUZE):
The range 6881 to 6999