Thought I would share my issue.
Had a early 2009 24 inch Imac. Linked to time capsule, backups without any issues.
Bought a new Imac , 27inch, 2TB on Dec. 26. Started up machine, it was fine. Downloaded data from time capsule, everything downloaded, good to go. This new machine had El Capitan. It seemed to be doing fine. Then I upgraded to Sierra, and soon after (within a day), started getting prompts about how backups couldnt be completed, if issue continued go to disk utility, and run first aid, and then ultimately recieved the message "Time machine completed a verification.....", just like other posters here.
I contacted apple care, long story short, they had me erase all my data (3 years ) from time capsule and start backing up again.(I did have data stored on a seperate hard drive as well, just in case) Did that, took several hours, and next day, the same thing started happening again.
The interesting thing is that I also have a macbook pro, using El Capitan, and it downloads backups to the same time capsule, without any problems!
Called apple care again, and long story short, they decided it was a problem with the OS (sierra), and did clean installs, resets, etc, and still no success. Ultimately they had me totally erase the hard drive, and at that point they kinda suggested to exchange the new computer for another new one. Apple store is only 5 minutes away for me.
Got a another brand new 27 inch Imac, 2 tb, and was able to get my information on it from the hard drive. This one already had Sierra on it. And soon after that, several issues popped up on trying to backups. First issue was that there was keychain issue(I never use keychain, which also had my email hosed up), some how that issue finally went away, and then the "Time machine completed a verification"......started again.
At that point, I connected another external hard drive and am having backups downloaded to it using time machine. Works perfectly, and at the same time, the Macbook pro is still downloading backups to the time capsule without any issues.
I probably have invested 5 hours with apple care in this, and still no resolution. Guess I will just have to use my workaround. Maybe a future upgrade of Sierra will fix it. At this point, I have no clue on what to proceed on.