Shortcodes in Comments
WordPress comments as far as I know don't render shortcodes.
If your theme use custom shortcodes you can't use them in comments. Also, with the new video and audio support for WordPress 3.6 you can not use them in comments.
Simply add this line to your functions.php of your theme and now shortcodes will be correctly rendered within comments.
add_filter( 'comment_text', 'do_shortcode' );
Shortcodes in Widgets
Yes, following the same principle you'll need to add a new filter to the functions.php file.
Try it first, put a shortcode in a text widget, your theme might already have this line. If the shortcode doesn't work, then paste the following snippet:
add_filter( 'widget_text', 'do_shortcode' );
Shortcodes in Excerpt
Yep. Even though I wouldn't recommend it. You see, I usually use this field for SEO purposes so I won't use any shortcodes in it.
However, if you need it, here it is:
add_filter( 'the_excerpt', 'do_shortcode');