Yeah, multiple asides makes sense to me because each note is really a standalone statement. But as Alex says, it does matter what the parent element is to establish the context of the aside. In every case I can think of where one of these notices would appear, it really should be in the context of "a side thought relating to the entire document" and not just to a single part of it. If it's inside an article or a section, it changes that semantic relationship (it's inside a section on the dashboard, for example).

So... if we want to be sticklers about semantics then maybe it shouldn't be an aside at all, since that element relies too much on its parent element to establish context. We could play it safe and make notices a generic div so they'll have no special semantics at all and their context wouldn't matter (though the div should still have the alert role for errors).