For those with this issue (your backup completes successfully but "some files were skipped", and the log shows something like "Backup encountered a problem while backing up file C:\Windows\System32\config\systemprofile\My Projects Error:(The system cannot find the file specified. (0x80070002))" -- the "My Projects" would be the name of a folder you added to a library you created), the fix is relatively simple.
- Either click the Change Backup Settings link from the error message, or open Backup and Restore and click Change Settings.
- Choose your destination drive.
- "Let me choose."
- Uncheck any libraries you've created.
- At the bottom under Computer, expand you drive and work your way to the folder(s) contained in the libraries you disabled in step 4. Check each one.
- Click next, make sure all your files are listed, and click Save & Exit.
- Try your backup - it should complete successfully, with no files skipped.