We had this same problem this past weekend, only in module 2 on a 5596.
In our case, we had rebooted our primary Nexus and found the following message immediately preceeded the BTCM error you noted:
%$ VDC-1 %$ %NOHMS-2-NOHMS_DIAG_ERROR: Module 2: Bootup diag detected major event: Forwarding ASIC failure: Ethernet2/9 Ethernet2/10 Ethernet2/11 Ethernet2/12 Ethernet2/13 Ethernet2/14 Ethernet2/15 Ethernet2/16
We replaced the module. A "show diag results module 3" would probably show you the same thing. However, I don't think the error message will show up until you reboot.
If your flapping Nexus is secondary, you probably won't notice anything major, but if it is your primary, it would probably affect your routing.