Yes, comments affect the Google ranking. When I say comments, I do not mean when you go to a blog or website and leave a comment and make a backlink to your website. I mean the comments people leave on your website. Comments on your website have always been important, but with the new Google update they get even more weight because Google translates this as a user experience. You visit dozens of websites today, but you probably will not leave a comment on any of them, you have to be provoked (positive or negative) to leave a comment, and as many the comments your site has, Google considers it a better user experience. If people on your website leave comments like: keep it going, good work, you rock ... Google considers it a spam. Google gives more value to longer comments, especially if people start conversation. So in order to improve your ranking, you have to provoke people positively or negatively to start a conversation in your comments.
To conclude: are comments decisive factor for the ranking NO, are they important factor YES.