// current user
$user = new WP_User(get_current_user_id());
// the custom field on the user's pages
$showintern = get_field('user_intern_yes', 'user_'.$user->ID);
// check if user has set $showintern field to "yes"
if($showintern == 1) :
// show stuff
endif;

function wpse28782_remove_menu_items() {
    $user = new WP_User(get_current_user_id());
    $showintern = get_field('user_intern_yes', 'user_'.$user->ID);
    if($showintern == 0) :
        remove_menu_page( 'edit.php?post_type=intern' );
        remove_menu_page( 'edit-comments.php' );
    endif;
}
add_action( 'admin_menu', 'wpse28782_remove_menu_items' );