If you click on the "new" icon on the thread title it will take you to the first new comment.
This is helpful, I didn't know you could click that.
There's no way to do what you want AFAIK. You might want to consider adding it to the new forum software requests. As-is, I just keep the tab open until I'm ready to get back to it, which is probably why my tab bar is always such a mess.
I'm a serial tabber, so I think this would make a mess of things even more so than they already are. I was just hoping for a quick way to do it in the forum. It seems the suggestion quoted above might be the best way to do it. That wouldn't help if you don't read all the new comments at once though. Especially for popular threads, I can't always read all the new comments in one sitting, so I was hoping for a way to mark where I left off in instances for times when I can read longer.