how do you prevent showing a particular category on the admin dashboard for specific user roles?

Based on the first Answer from Mike Schinkel. For testing purposes in a default installation, the category is “Uncategorized”.

add_filter( 'list_terms_exclusions', 'wpse_59652_list_terms_exclusions', 10, 2 );

function wpse_59652_list_terms_exclusions( $exclusions, $args ) 
{
    global $current_screen;

    if( 'post' != $current_screen->post_type )
        return $exclusions;

    if( !current_user_can('delete_others_pages') )
        return $exclusions;

    return $exclusions . " AND ( t.name <> 'Uncategorized' )"; 
}