Serious Time Machine bug on Mountain Lion
Some of us have seen a few cases of a pretty nasty problem with Time Machine backups on Mountain Lion.
In the worst cases, the backups could not be used to do a full system restore from recent backups -- they didn't appear on the selection screen that shows only "complete" backups.
Plus, they're not recognized as backups by Setup Assistant or Migration Assistant. They don't even appear on the Select the Source or Select Your System windows.
In those cases, the top-level System, Library, and (hidden) private folders weren't backed-up at all (and in at least one other, Applications as well). But all backups complete normally, and Verify Backups from the Time Machine menubar on network backups, and Verify Disk or Repair Disk via Disk Utility do not show a problem (because what's there is intact; those can't tell what's missing.)
(In addition, we've seen a few threads where backups were unexpectedly large, sometimes all of them, sometimes just some, intermittently. In at least some of those cases, one or more of those folders was getting backed-up in full. We don't know if this is really the same problem, but it sure is suspicious.)
The problem seems to be with the Time Machine preferences file being damaged somehow; the fix is easy -- do a "full reset" of Time Machine, per #A4 in Time Machine - Troubleshooting. It won't change existing backups of course, but new ones should be ok.
However, as we have no clue as to the cause yet, we need to be sure Apple knows about this, in great detail, so I'm asking for some folks who are having these problems, and are fairly comfortable with the Finder at least, and following directions to do other things you may not be so familiar with, to help us collect information and file Bug Reports with Apple before running the fix above (as that will destroy the evidence).
If you're having this problem, and your Mac is still usable, and you're interested, please post back and we'll supply instructions.
If you're having the problem and just want to run the fix, by all means do so, but please don't post back with just a "me, too" post, unless you have something significant to add -- this thread may get long and those won't really help.
But if you're having a different problem, please do not respond to this thread. Start a new one, instead. If you're not sure how to do that, please go to the main Apple Support Communities page; some Tutorials are listed at the right. They'll show you how to get started.