I don't know of any way to block a thread (not even with my moderator rights).
I always use "view unread" when I visit the board, whether it's through my browser or using TapaTalk on the phone. I just skip over threads that don't interest me,and when I'm done I click on 'mark as read'.
You can subscribe to specific threads and you can follow users (at least on TapaTalk you can).
Hope that helps a bit.