Time Machine: Error occurred while creating the backup folder

Question

Mac Mini 2.53 GHz, 8 GB DDR3
OS X 10.8.4
Time Capsule 1 TB, connected via ethernet
Airport Utility 6.3.1 (631.4)
"Time Machine Error.  Unable to complete backup. An error occurred while creating the backup folder."
I believe my Time Capsule is out of space and isn't removing older backups to create space for itself.  Time Machine preferences says only 98 MB available on the 1 TB volume.  I have used Pondini's superb troubleshooting page with the following results:
A1: Time Machine Buddy Widget.  Partial log from backup attempt:
Backing up to: /Volumes/Time Machine Backups/Backups.backupdb
Failed to create progress log file at path:/Volumes/Time Machine Backups/Backups.backupdb/Macmini-34159E18D208 (4)/2013-04-04-223516.inProgress/.Backup.400571203.603238.log.
Event store UUIDs don't match for volume: Macintosh HD
Error: (Error Domain=NSCocoaErrorDomain Code=640 "You can’t save the file “598C5622-100E-456A-89AF-DEBC87A6CA89” because the volume “Time Machine Backups” is out of space." UserInfo=0x7f88a330cef0 {NSFilePath=/Volumes/Time Machine Backups/Backups.backupdb/Macmini-34159E18D208 (4)/2013-04-04-223516.inProgress/598C5622-100E-456A-89AF-DEBC87A6CA89, NSUnderlyingError=0x7f88a33056a0 "The operation couldn’t be completed. No space left on device"}) Creating directory 598C5622-100E-456A-89AF-DEBC87A6CA89
Failed to make snapshot.
Backup failed with error: 2
Ejected Time Machine disk image: /Volumes/Data/Macmini-34159E18D208 (4).sparsebundle
Ejected Time Machine network volume.
A4: Full reset of Time Machine.  Done, did not change error from occurring on next backup attempt.
A5b: Verify backups on Time Machine.  Done, successful (no problems).
C10: Also attempted switching out ethernet cable and tried different ports on the Time Capsule, to no effect.
I have no exceptions listed in Time Machine preferences (under Options) and the box for "notify when deleting old backups" is UNchecked.
Any suggestions would be most appreciated!!

Answer 1

grifftastic wrote:
I believe my Time Capsule is out of space and isn't removing older backups to create space for itself.  Time Machine preferences says only 98 MB available on the 1 TB volume.
"You can’t save the file “598C5622-100E-456A-89AF-DEBC87A6CA89” because the volume “Time Machine Backups” is out of space."
Yes, it's so full it can't get started -- not even far enough to start deleting old backups.
If you have other data there (not usually a good idea), move some of it elsewhere temporarily, and try again.
If not, manually delete a couple of old backups, and "compact" the sparse bundle, per Time Machine - Frequently Asked Question #12.