Version 1.4 has just been released and is available from the WordPress.org theme repository.
There has been substantial changes in the theme's navigation menus, so before anyone come in here screaming because their menus look wacko, I thought I'd write this heads up.
The new primary menu now supports description for each menu item in the top level menu (i.e. not the dropdowns). Unfortunately, the description field in the WP Admin > Appearance > Menus screen isn't available by default. Couple that by the fact that WordPress automatically assigns the excerpt as the description, each of your menu item now will have a long description underneath.
This is of course undesirable. The description in the theme was meant to be just a few words. See the demo site on how the menu is intended to look like.
To set up your own custom description for each menu item, simple click on the "Screen Options" at the top right of the WP Amin > Appearance > Menus screen, and tick on "Description". Once you've done this, each menu item now will have a "Description" field which you can edit. If you don't want the description to be displayed at all, just simply delete the descriptions for all top-level menu items of your primary menu.
Note that you will need to concern yourself only with the top-level menu item of the primary menu, as only these will show the description. All other menu items (dropdown menu items, secondary menu, and footer menu) will not show up any description.
See screenshots below for visual clarification.
UPDATE: As of version 1.4.1, menu item that has description longer than 50 characters will not be shown. This should also prevent the undesired long excerpt that WordPress automatically assigned to menu items as their description from being displayed.
UPDATE 2: As of version 1.5, there's an option to completely disable the menu description in Graphene Options > Display > Navigation Menu Display Options > Disable description in Header Menu.
How the new navigation menu is intended to look like: