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I've encountered this too and agree that the current behavior leaves room for improvement.

I wouldn't want to see an automatic "dismiss all" action when you look at your notifications.  This is what SE does, and if you're active on several sites or just have a lot of stuff come in at once, it's too easy to miss seeing (or see but miss responding to) some of them.  I think I would prefer to see them grouped by post (your last option) -- if you're going to read one of the five new comments, you're probably going to read all of them while you're there.  Treat that as a group.

Different posts, however, should be different notifications (or notification groups), even if they're all in response to the same thing.  If I get several new answers to my question, I want to consider each of them individually, and reviewing one might lead me to check sources or do other investigations before I even look at the next one.  "3 answers to your question" should not be a notification group the way "5 comments on your answer" would be.

"Mark all as read" would also be useful to have, and if grouped notifications are too hard then let's at least do that.  I'd rather avoid clearing notifications based on what we *think* the user has seen; who knows whether and how far someone has scrolled the page?