Time Machine on Time Capsule backup verification never seems to complete
Solution 1:
Since the verification process is akin to running fsck
the filesystem check utility, this is the thing that will repair the backup or pronounce it dead.
If it fails too many times, you will then be left with a read-only Time Machine directory that you could clone somewhere else, restore the files you care, or wipe and start over.
Sadly, you are seeing all the progress that is normally available without running the tmdiagnose
tool to collect detailed status and log when you ask Apple or a technician to help with time machine problems.
In most cases, I would say pick a time you can afford to be without backups (a day, a long weekend, a week) and set the Mac to not sleep and let it chug and see if it finishes. At the end of the period, you can decide to clone off the data to an attached USB drive just in case you need to retrieve something or just wipe the disk and start over.
Have you rebooted your Mac and run a filesystem check (or safe boot) to make sure your Mac doesn't have any directory damage?
Solution 2:
There is possibly another way to handle this (had the same problem the other day on a system running Yosemite: go into System Preferences > Energy Saver, and set the sleep time to 3 hours or longer. Once I did this, the verification ran all the way through successfully.
Per a user on another thread (lost the link), it can sometimes be due to cross-linked files in the volume.
At first, I had assumed the worst, but after this one change, all appears OK on my system now.