Example: I'd like to hide Bindings of the Windseeker, because I don't really care about getting Thunderfury. And when I finish Molten Core I'd like it to be removed from my list, not still there because I still haven't gotten Thunderfury.

Unfortunately there won't be any ability to blacklist anything. All The Things is first and foremost a transmog collecting addon which Thunderfury is one of those items. Once you collect it on a toon however it will vanish from all of your other toons.