Actually, the more events happening on that page, it signals the search engine that the content could be very relevant to the topic, and hence, it slightly gives a better overall signal on your site on the SERP ranking.
However, if the comments are spammy, and filled with links, etc, then that would be the wrong signal being sent to the search engine, as it would simply get your site marked as a splog.
But good comments, relevant and refreshing content would definitely add a bonus to your site's signal in the process - but I doubt you can edit all the comments on your site.
Depending on your comment system, you could customize it by adding a 1-2 sentence guide as to how to post things you would approve. Set all comments to moderate (so they don't get published until you clear them), and all comments not meeting your criteria should be deleted,, or set to auto delete after a few weeks.