Exporting my Omega subtheme's settings resulted in the error message:
File temporary://fileH5qXui could not be copied, because the destination directory sites/all/themes/[themename] is not configured correctly.
I tried several different chmod values on the directory and the info file, but it turned out the problem was that the user with ownership of the subtheme's directory needed to be apache. A simple chown fixed it.
Apologies if this issue is mis-filed. The Omega documentation doesn't seem to go this in-depth so I didn't feel comfortable adding it there. Just trying to help out other Omega users who might have had the same problem.