From the blog post announcing the new notifications tab:
Since notifications aren’t as important as inbox notices, whenever you have unread inbox messages we’ll display the red inbox indicator rather than the gray notification indicator. Of course, once you open the drop down you’ll see that you also have new notifications.
Moderator messages currently fall under the category of "notifications", but I contest that those are far more important than even our regular inbox replies. Since they're reserved for serious issues, it only makes sense that they request immediate attention from those involved.
The ice-blue icon that currently represents notifications is barely visible on the gray Stack Exchange navigation bar. This is mentioned in New "Notification" colour isn't obvious. In fact, I'm noticing that since the introduction of the notifications tab and the incredibly hard to see icon, less than a third of the moderator messages we've sent in the past week have been read on our site.
(I don't know if that's a cause for concern among others because granted, mod messages are also sent as emails to users who have an email address on record so they'll probably receive and read them. But users who for whatever reason don't have associated emails may not end up seeing the messages on site at all, because the notifications aren't obvious.)
Anyway, besides changing the color of the new notification icon, which would be great, can we have moderator messages show up as red like all other inbox replies to the users involved? I suppose it's alright if they show up as regular notifications for other moderators who aren't directly involved in the conversation, but to those who are, they are very important.