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I'm afraid I don't know what to do about this, but here are the parts of the output that look especially important:

1: The top line is

/Applications/Sage-4.7.2-OSX-64bit-10.6.app/Contents/Resources/sage/sage

This is the command you can type in the Terminal to start the command-line sage instead of the notebook.

2: The OS Error may be a partial explanation of why you have to start Sage with root access:

OSError:  ** Error trying to create the Sage tmp directory in your home directory.  
A possible cause of this might be that you built or upgraded Sage 
after typing 'su'.  You probably need to delete the directory $HOME/.sage.

If you won't lose anything valuable, you should follow these instructions and delete the .sage directory. WARNING: This is the directory that stores all of your sage-related data. Deleting it will delete all of your saved notebooks. Before you do this, you should export anything you don't want to lose to a .sws file. When you're ready, you can delete the directory with

sudo rm -rf ~/.sage

Once you've done that, try to start Sage, but not as the root user: To ensure that you are no longer functioning as root user, you could quit the Terminal and then reopen it. When you have done this, type the command to start Sage and it will automatically create a new .sage directory for you -- this time with (hopefully) the correct permissions.

Good luck!