You could highlight the first comment of each new subthread, or have an option to collapse the threads down to that point. You could even have a single button that scrolls down to each consecutive new comment chain.
But it would probably have to be a lot more minimalistic than a new sidebar.
Ok, that sounds like the Chrome extension that adds "orange lines next to new comments since your last visit", mentioned in this comment (on this same page): https://hackertimes.com/item?id=12664187
A button to scroll down to the next unread comment thread sounds interesting.
But it would probably have to be a lot more minimalistic than a new sidebar.