In wp-twitter-widget.php, on line 632, appears the following code:
wp_enqueue_script( 'twitter-widgets', 'http://platform.twitter.com/widgets.js', array(), '1.0.0', true );
To avoid mixed-content warnings when embedded in a WordPress installation served by HTTPS, it should read as follows:
wp_enqueue_script( 'twitter-widgets', (is_ssl() ? 'https' : 'http') . '://platform.twitter.com/widgets.js', array(), '1.0.0', true );