Give wp_nav_menu() a different class then default. In some cases themes style on the class 'menu'. What result in possible weird behavior.

gistfile1.php

<?php

class Nav_Menu_Widget_Classname {
	public function __construct() {
		add_action( 'widget_display_callback', array( $this, 'menu_different_class' ), 10, 2 );
	}

	public function menu_different_class( $settings, $widget ) {
		if( $widget instanceof WP_Nav_Menu_Widget )
			add_filter( 'wp_nav_menu_args', array( $this, 'wp_nav_menu_args' ) );

		return $settings;
	}

	public function wp_nav_menu_args( $args ) {
		remove_filter( 'wp_nav_menu_args', array( $this, 'wp_nav_menu_args' ) );

		if( 'menu' == $args['menu_class'] )
			$args['menu_class'] = apply_filters( 'nav_menu_widget_class', 'menu_widget');

		return $args;
	}
}
$GLOBALS['nav_menu_widget_classname'] = new Nav_Menu_Widget_Classname();