Eh gonna necropost here too because these errors were annoying to get rid of.
Not sure where to put the warning, so right up top it is: doing as I did below will remove all System Restore points/previous version backups of files that Windows had saved there, any/all Shadow Copies I believe, old CHKDSK log information, the Transaction Log for Resource Managers, and whatever else Windows might store in there that I can't remember or didn't care about.
Read up on the System Volume Information folder if you'd like to know exactly what lives there.
Note: If you've created new Restore Points/previous versions of files images, etc. with Windows since having these errors (or more accurately, since replacing your drive), those restore points etc. will be nuked by doing as I am going to describe.
I'm not certain if you can repair this folder more surgically, but potentially you could go through the steps to take ownership of it, allow yourself full access to it, and only delete the files/subfolder used by the Resource Manager Transaction Log, but idk if that will actually be sufficient, or if there's another related file/folder to also nuke, or if security permissions weren't set correctly within one of those folders or files, etc.
What I have is a solution that takes you back to fresh square 1 Windows image backups/system-restore-point-wise. If you don't care about old backups, and will just create a fresh backup/restore point once you've rebooted, then this is a good solution for you.
So! After trying all available solutions, I found deleting the System Volume Information folder in Safe Mode, restarting normally and letting Windows rebuild it did the trick. You will get one more set of errors (correctly), because you deleted the folder used to check file transactions are in order, so it actually wants rebuilding this time, but there shouldn't be any errors after it's rebuilt the folder/index. BTW doing this restores the proper security permissions for the System Volume Information folder and its subfolders- it's supposed to tell the user Access Denied :)
I was using Win7 but I expect it applies to other versions, particularly if you did as below.
The cause of the problem in my case was that I had copied over the System Volume information folder when cloning to a new SSD, hoping to preserve Windows' Previous Versions of files/folders, but not only did that not work (everything said I had no previous versions or System Restore images), I also got NTFS errors any time VSS was invoked during backup/imaging operations. Those do happen in the background, so you could mistake it for random.
Newly created backups and Previous Versions images still seemed to work, but things were not technically in a fully functional state.
I'm guessing it was the same deal for the OP. Hope this is useful to some peeps :)