I, too had this same problem. 2T Seagate FW800 external which I have used for about 18 months flawlessly until this update. I started getting Time Machine errors - "unable to create backup folder". In troubleshooting that, discovered multiple drive errors using Disk Utility verify, but the repair failed as described in this thread.
I was unable to even unmount the partition - getting a files in use type error. Upon looking at the files on the backup partition, I found the current backup file with the suffix ".in_progress". At that point I could not delete the file, since the system saw the file as "in use"
So I looked both ways to see if anyone could see me, then I simply disconnected my external drive. Dangerous, I know - and I am looking forward to reading all about it. BUT - to continue...
After reconnecting the drive and letting it mount, I was able to delete the file. Now, disk utility shows no errors and Time Machine is currently backing up.
I have absolutely no idea if this will fix anything. But I will have a current backup in a few minutes.