Does Time Machine check that old backed up files are present and not corrupted?
If you hold the "Option" key while clicking the Time Machine icon in the menu bar, there is an option "Verify Backups".

If the Time Machine icon is not in your Menu Bar, go to System Preferences, Time Machine, and tick the "Show Time Machine in Menu Bar".

I can't see any other way to get to the "Verify Backups" other than through the item in the menu bar.