I very seldom do, mostly because I don't have many friends come over and say anything on it. And when I do, I just read it once and leave it alone for the automated messages to overlap them.
I never look at it as I just get overwhelmed by the several hundreds of posts I missed ^^' love when people take care of theirs and doodle cute stuff. Me and my time hopping just ruined that option forever.
I only really look at it if I've had others in my town recently. I also don't really bother with cleaning it up to bring important messages to the top because I can just screenshot them.
I used to check it super regularly, anytime there were birds, but later on in my New Leaf playthrough I got sick of the Nooklings' advertisements and only checked periodically to clear them out.
I also used to post mayoral announcements/decrees/etc. on the bulletin board for my villagers lol. I think one time I announced a temporary ban on Hide and Seek because my grass wear was getting bad and they all kept wanting me to play it with them.
I read it whenever there are birds on it, yes. I never really did much online play so I didn’t have messages from friends or anything like that. But I’d hate to miss a villager’s birthday on accident, or some kind of special event.
I’m a bit OCD about notification icons… They must be cleared at all times. Even if I just open them for a second and close them again to get rid of the icon/bird/flashing mailbox etc.
Whenever the bird or owl shows up. I know what to expect, but why wouldn't a resident read the current notifications? I also enjoy the notes that comment on the weather or announce seasonal changes, they add some pleasant atmosphere. I still want actually frozen ponds, though.