Many older homes have plaster walls instead of wallboard. This becomes an issue when trying to hang a heavy object, like a framed mirror. Plaster is applied over lath, a series of thin boards, which makes finding a stud more difficult. Many older homes do not use uniform stud spacing. However, because of the inherent strength of the plaster/lath combination you can hang heavy items with the right tools and know-how.
Buy a molly bolt. Molly bolts come in a variety of sizes. For a heavy object like a mirror choose a larger bolt. The bigger the bolt the more weight it can handle. For a heavy framed mirror you'll need two bolts.
Pre-drill two holes about six inches from the centre point where you want the mirror to hang. Take into account that the mirror will actually hang higher than this. Use a drill bit the same diameter as the molly bolt; the hole should be as deep as the bolt's length. With a plaster wall you will want the hole to go through the plaster and the lath, about three inches.
Insert each bolt into its hole. It has a pointed end and spacers which spread into wall as bolt is tightened. The head should be flush against the wall. Tap it gently with a hammer to get it all the way into the wall.
Insert the screw and turn it clockwise until the top of the bolt is against the plaster wall. You will feel resistance as it flattens out against the back of the wall. Back the screw out a few turns so the mirror has a point to hang on.
Loop a wire through two supporting hooks on the back of the mirror and securely tie off the ends. Hang the mirror by hooking the wire on the screws in the molly bolts.