It is not a bad idea to showcase the content that sparks discussion on your site. It helps you build a community around the discussions on your website, which is more user engagement and more trafic for your website.
You need to do is install and activate the WordPress Popular Posts plugin. Upon activation, simply go to Appearance » Widgets and drag and drop WordPress Popular Posts widget to your sidebar.
Select Comments under Sort Posts By option to display your most commented posts. Choose a time range from last 24 hours, last week, last 30 days, or all time. Select All Time in the time range to display your over all most commented posts.
The widget also allows you to choose post type, which is very useful when you are using custom post types on your site. In some other options, you can choose whether to display thumbnail, comment count, or post excerpt etc.
WordPress Popular Posts is delivered with a shortcode that you can use to your posts or pages in order to display your most commented posts. The shortcode comes with the same configuration parameters. To display it, for example your all time 10 most commented posts, you would better use a shortcode like this:
[wpp range=all stats_comments=1 order_by=comments post_type=post,page limit=10 wpp_start=<ol> wpp_end=</ol>]
To see a full list of parameters you need to go to Settings >> WordPress Popular Posts and then click on FAQs section. Scroll down to the shortcode parameters question then click it.