Time Machine disk filled up, then got corrupted

I got an error msg saying that the Time Machine disk was full. Under normal circumstances TM is supposed to just overwrite the oldest backup. But in my case I started getting all kinds of errors from “The backup disk could not be mounted” to “The backup volume is read only”. I tried running Disk Utility to repair the sparse bundle, but to no avail (it kept reporting the invalid sibling link error). I even tried using Disk Warrior to repair (rebuild) the sparse bundle backup directory, but that also did not work. The last resort was to use the solution found here. While TM was mounted and while I could see the backup disk, I disabled TM and ran the following:

hdiutil attach -nomount -readwrite (server-name)_(mac-address).sparsebundle

This command took a while to return, but when it did it showd:

/dev/disk1            BackupOf(server-name)

I then ran

fsck_hfs -rf /dev/disk1

And this took a few hours (not sure how long exactly, I just let it run overnight). This produced the following:

** /dev/disk1**
Checking Journaled HFS Plus volume.**
Detected a case-sensitive catalog.**
Checking Extents Overflow file.**
Checking Catalog file.**
Rebuilding Catalog B-tree.**
Rechecking volume.**
Checking Journaled HFS Plus volume.**
Detected a case-sensitive catalog.**
Checking Extents Overflow file.**
Checking Catalog file.Incorrect number of thread records(4, 13716)**
Checking multi-linked files.**
Checking Catalog hierarchy.
Invalid directory item count(It should be 0 instead of 1)
Invalid directory item count(It should be 3 instead of 4)
Incorrect folder count in a directory (id = 3795486)(It should be 0 instead of 1)**
Checking Extended Attributes file.**
Checking multi-linked directories.**
Checking volume bitmap.**
Checking volume information.
Invalid volume free block count(It should be 37267681 instead of 37310834)
Volume Header needs minor repair(2, 0)**
Repairing volume.**
Rechecking volume.**
Checking Journaled HFS Plus volume.**
Detected a case-sensitive catalog.**
Checking Extents Overflow file.**
Checking Catalog file.**
Checking multi-linked files.**
Checking Catalog hierarchy.**
Checking Extended Attributes file.**
Checking multi-linked directories.**
Checking volume bitmap.**
Checking volume information.**
The volume Backup of Bhaal was repaired successfully.

At this point I re-enabled TM and initiated a backup. Voila! It worked! Here’s the oldest backup to date: