We came across this 0x80070718 not enough quota error on a Windows 7 Pro machine recently and just wanted to explain what happened.
A user was trying to save attachments from Outlook on an Windows laptop when they were out of the office but was seeing an 'unable to save' error trying to save to 'My Documents' but could save elsewhere.
I tried creating a new file in the folder which seemed to work but saving the attachment did not. I checked disk space and all was OK but then saw that the 'My Documents' was an offline folder copy of the 'My Documents' on her PC in the office. Once this was discovered I went into the Control Panel>Sync Centre and saw that she only had 127Kb left in her offline files quota. Once I had increased the file quota size the issue was solved.
Just so you know...