How to make Mutter default window manager

Press Alt + F2 and enter gconf-editor. Navigate the tree menu to desktop > gnome > session > required-components. Now, replace the windowmanager key with the window manager of your choice. Just replace gnome-wm (or metacity) with mutter.

Another possible solution:

You could add mutter --replace to System > Preferences > Startup Applications which opens gnome-session-properties program: