Hey lil. On the top right of your notification page (click that orange hubwheel) there is a 'dismiss all notifications' link. That should do it. Alternately you can go through and click 'dismiss' under each thread individually.
mk, what do you think of this idea? The orange hubwheel turns not-orange when you visit notifications (and not just when you dismiss them). If it turns orange again, it means there are new ones. I always dismiss all, because that's the only way to get it to change state on a new notification; but why must it be this way?
Since this is likely to lead to people leaving lots of things in their notification page, you may want to consider a rule like "notifications that have been read disappear after n days". That way, if you dismiss nothing, your notifications page shows you your last week (or month or whatever) of activity.
Is it possible to not receive notifications from comments on threads I've saved that I'm not associated with?