I am saying it is impossible to get notifications in a consistent manner just from specific sub-threads.
Imagine that someone started a new thread A (like this one "Stuff That Should Be Improved"), and later several sub-threads B, C (e.g. "Get Notifications from Sub-threads"), D developed from it:
You are interested in following only a sub-thread C and you want to get notifications from it, but not from A, and not from B and D. To do so, everybody who participate in the discussion C should use Reply button under first C post. People usually don't do that on forums and mailing lists. They are replying to the end of everything (the main A thread), or they are replying to something in subject B and also referring to something in C... and so on. Hence, I don't see algorithm which can recognize everything connected to C, but not to other sub-threads or the main thread and that's why you cannot get notifications only for C. One way to solve this is to extract B, C and D to independent threads/subjects and to use Tracking option... then you could track only C if you want, but as long as everything is dumped in a single thread, I don't see how to consistently follow only one sub-thread without imposing rigorous discipling by moderators who will fork/remove everything that is even slightly off-topic