Time Machine Backup Stops Unexpectedly

Question

My Time Machine backup has worked pretty much without a glitch for years, but two days ago it stopped working.  About the time it stopped working, I was burning a number of discs with iDVD.  Some of the burns were not successful and required that I reboot the computer (iMac updated to 10.8.3 this morning) in order to get the disc to eject.
When Time Machine starts running it says that there is 62GB of 1TB available on the backup drive and that there is 1.19GB to be backed up.  At some point, the amout of data to be backed up starts increasing and eventually gets to a point where it exceeds the 62GB available.  Then this message appears:  "The backup disk ran out of space unexpectedly. Time Machine will try to make more space available by removing expired backups during the next scheduled backup."  It looks like the oldest backup is from June, 2010 and I see no problem with deleting these old backups, if necessary.
I suspect that iDVD has created some file somewhere that needs to be deleted, but I don't know where to look.  I have updated my OS and rebooted the computer, but this has not helped.  Does anyone have any ideas?  Thanks!

Answer 1

If you have more than one user account, these instructions must be carried out as an administrator.
Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad. Click Utilities, then Console in the icon grid.
Make sure the title of the Console window is All Messages. If it isn't, select All Messages from the SYSTEM LOG QUERIES menu on the left. If you don't see that menu, select
View ▹ Show Log List
from the menu bar.
Enter the word "Starting" (without the quotes) in the String Matching text field. You should now see log messages with the words "Starting * backup," where * represents any of the words "automatic," "manual," or "standard." Note the timestamp of the last such message. Clear the text field and scroll back in the log to that time. Select the messages timestamped from then until the end of the backup, or the end of the log if that's not clear. Copy them (command-C) to the Clipboard. Paste (command-V) into a reply to this message.
If there are runs of repeated messages, post only one example of each. Don't post many repetitions of the same message.
When posting a log extract, be selective. Don't post more than is requested.
Please do not indiscriminately dump thousands of lines from the log into this discussion.
Some personal information, such as the names of your files, may be included — anonymize before posting.