When you receive unopened mail (when finishing a research topic, for example), the "mail client" button on the geoscape screen starts blinking. However, sometimes when loading a game back to an earlier point of time where I have no mail I haven't already seen, that button is still blinking.
I've attached a savegame. Progress time until the current research project "UFO Theory" finishes, then load the game without looking at the new mails. When I do that, the "mail client" button still blinks, even though it shouldn't.