Highlight a Post on archive page if it has a new comment?

You need to do a couple of things. To find new comments you need to be tracking visitiors. If you’re capturing last login time that’d be great.
Then you need to edit your template to check your comments before dissplaying the content. Alter you comments query and here and if there’s new comment since the last login add a class to the post div element. In your css manipulate the post display any way you like.

Update: I found an easier way.
I adapted this code from here You still have to get the last login time yourself using some plugin or other way of getting a timestamp. Maybe set a cookie? I just added an if statement to wp_get_comment_date and if it’s newer than the last login flag the comment.

Sorry I can’t set up a working sample . . . I just don’t have the setup right now.

<?php
        $num_comments = get_comments_number(); // get_comments_number returns only a numeric value

        if ( comments_open() ) {
            if ( $num_comments == 0 ) {
                $comments = __('No Comments');
            } elseif ( $num_comments > 1 ) {
                if ( strtotime(get_comment_date( 'yyyy-mm-dd' ) ) > strtotime($get_last_login_tile ) ) {

                    $comments = $num_comments . __('<b> New Comments Since Last Login</b>');

                } else {
                    $comments = $num_comments . __(' Comments');
                }
            } else {
                $comments = __('1 Comment');
            }
            $write_comments="<a href="" . get_comments_link() .'">'. $comments.'</a>';
        } else {
            $write_comments =  __('Comments are off for this post.');
        }


        ?>