I tried 1.8.2 and noticed:
It didn’t work at all just after I upgraded the plugin.
When I logged out, it suddenly began to show a pretty nice live preview.
It seems live-comment-preview.js assumes author and email textfields in the comment form. My comment form omitted these fields because I logged in as admin, so the javascript didn’t work.
I modified my custom theme to add author/email hidden fields so it works fine now. But I’d like to see this plugin working without such a trick.