Time Machine hasn't been backing up the full system since before 10.8.3 Look at your hard drive. Now look at me. Now look at a recent snapshot in your Backups.backupdb directory from after the 10.8.3 release (March 14th-ish); now look at mine. Hopefully, your snapshot doesn't look like mine, because if it did, you'd notice that Time Machine hasn't been backing up /Applications, /Developer, /Library, /System, or /private for the past two months.

Um, what??? There's no setting related to this in System Prefs, and I actually have 10 GB still free on the drive, and I'm reasonably certain this started happening after installing the 10.8.3 update. Except for individual user files, Time Machine is completely useless to me right now and all of the backups done in the past two months are invalid for system restore.

Before 10.8.3:

ligeti:Macintosh HD nick$ cd 2013-03-18-003447/Macintosh\ HD/
ligeti:Macintosh HD nick$ ls -a
.               Users
..              Volumes
.DS_Store           bin
.DocumentRevisions-V100     cores
.com.apple.backupd.mvlist.plist etc
.file               lib
.vbt5               mach_kernel
.vol                opt
Applications            pbcl.db
Developer           private
Games               sbin
Library             tmp
Network             usr
System              var


After 10.8.3:

ligeti:Ligeti nick$ cd 2013-03-25-001307/Macintosh\ HD/
ligeti:Macintosh HD nick$ ls -a
.               Users
..              Volumes
.DS_Store           cores
.DocumentRevisions-V100     etc
.com.apple.backupd.mvlist.plist lib
.file               mach_kernel
.vbt5               opt
.vol                pbcl.db
Games               tmp
Network             var


Excuse me while I fire up Carbon Copy Cloner, but does anyone have any light to shed on this? Can anyone comment as to whether they are or aren't experiencing this on 10.8.3?
You aren't supposed to browse the Time Machine directory tree directly. Try entering Time Machine from the Finder and just look for those folders from there.

If you're sure that those folders aren't in the backup, check System Preferences -> Spotlight -> Privacy.
To check all the excluded items, you can execute this command from Terminal:

sudo mdfind "com_apple_backup_excludeItem = 'com.apple.backupd'"


It will display a list of excluded paths.
If you can't identify the source of the issue, I suggest to wipe the backup drive and to make a new backup.