The only workaround I've found is to read through the threads I want. Then, once only unwanted threads show up on pressing "Unread posts," hit "Mark Read" and they won't show up the *next* time you press "Unread posts."
What's your ratio of wanted vs. unwanted threads (the software actually calls them "topics")?
I note that within the pages of a topic, there's a pair of buttons (one on top, one at the bottom) labeled "Mark unread" whose URLs actually contain "...?action=markasread;sa=topic;...". My assumption is that the button's plain mislabeled, and marks the entire topic
read, but I didn't try it out yet. So, if there's only a few topics you're not interested in, you could click them open from "unread posts" just the same, and then dismiss them with just one scroll+click+tabclose.