My idea is: Like the shout box, a box comes up which has your most recent message written in it. And every time you get a new message, the new message replaces the old. It would say at the top of the box - "you have unread log messages" and will stay like that until you actually go to your logs and check them. The box would be a link to your logs. If you haven't had any new messages since you last looked at your log page then the box won't be there.
Also, if you are worried that you might miss messages because you think you've read them all without going to the log page, there could also be a number written in the box which tells you how many messages have come in since you last accessed your logs.
To make it easier to know when a new message has come in if the box is there and you don't check your log page, you could click on a "read" button on the box to acknowledge you have read that message in the box, and the box then disappears.
You would also be able to change your preferences as to whether or not you want this box, and if you want the box to disappear after you have looked at your log page.
If this was implemented it would mean that when you are hunting etc. you wouldn't have to open up another page every time you get a message.
So, if this was implemented you could be hunting away on the world page, a message appears in the side panel, you glance over, read it, then click the "read" button, or just leave it, and continue hunting with barely a pause.

