Remove “You are using WordPress 3.2.1” from Right Now Dashboard Widget

There is a trick to get rid of this using the gettext filter for translations.

This basically replaces it with nothing.

add_filter('gettext', 'remove_admin_stuff', 20, 3);

function remove_admin_stuff( $translated_text, $untranslated_text, $domain ) {

    $custom_field_text="You are using <span class="b">WordPress %s</span>.";

    if ( is_admin() && $untranslated_text === $custom_field_text ) {
        return '';
    }

    return $translated_text;
}

Be aware that the version also shows in the footer and several other places, if you want a good breakdown check out the source of this plugin, it seems to have covered more or less all of it, http://wordpress.org/extend/plugins/hide-wordpress-version/