Unfortunately, I don't believe SMF has thread subscription in the same sense as phpbb, vbulletin, and all the other forum software. The closest thing it has is the "Show new replies to your posts" link at the top, but that only shows threads that you've actually posted in and there seems to be no way to selectively add arbitrary threads to the list. The notify button will only send you email notifications and will not add the thread to that list. In both cases, you can only find the thread again if it becomes active again with new posts. There just seems to be no way to maintain a list of interesting threads like you do on other forums.
Some time ago I spent a few minutes googling for a mod for this so I could ask Dave if he would mind installing it, but I failed to find it. I had expected it to be right at the top of the search results, so it's possible that I just wasn't prepared to look hard enough.