Actually, you can only prevent the pop-up notificaton that appears when you've got a new message. You can't stop the box from flashing unless you read the new message. I think, however, that the box should stop flasing just as soon as you open your inbox, not after specifically opening the new message. For exmaple, if one of my highscores gets taken in the arcade, reading the summary of the private message tells me everything I need to know; yet I still need to have clicked and opened it to get the box to stop flashing. The same goes for private messages that only consist of one or two lines.
Eh, you get the idea. :tup: