How serious is mildew on the ceiling of the top floor of a house?
It probably means that you have a hole in the roof that was large enough to drip enough water to stain the ceiling (which doesn't take much, really) but small enough so that the amount of water dripping through is contained by the ceiling and does not leak through inside the room.  I would try to get the coordinates of the stain on the roof and get on the roof, project it there, try to find the hole and patch it.