OK, it does appear to be an issue with jumping up too many versions.   I was successfully able to update the firmware on all NICs to Version 6.4.4 using NETW_FRMW_WIN_R309327.EXE, and after a restart, was able to get them all to successfully update to Version 6.4.5 using the latest R319248.EXE.
I've got PE M600 blades in a PE M1000e chassis.  I recently attempted to updated the firmware of the Broadcom 5708 NICs on one of my M600's, using the NETW_FRMW_WIN_R319248.EXE file provided by the Dell support download page for my service tag. I ran this file on the blade (running Win 2008 R2) and it only completed successfully for 2 out of the 6 NICs.  Looking at the log files, the only difference I could find is that the NICs where the update succeeded show a subVendorID="1028", whereas the ones that failed have subVendorID="105b".  What the heck?  PE M600 iDrac Firmware: 1.55 (Build 2) CPLD Version: 1.01 BIOS Version: 2.4.0 Broadcom BCM5708s NetXtreme II GigE:   Old FW Version = 4.6.8   New FW Version = 6.4.5       
M600 Broadcom 5708S firmware update error