Sometimes your mirror is a beast. It’s the kind that came with your grandmother’s house and might outlive us all. In that case, try removable wall putty—the blue sticky stuff that looks like silly putty for adults. Roll it into small balls, press them onto the back of the mirror, and then smoosh the whole thing against the wall.
Putty works best for lightweight mirrors under five pounds. It’s like using Play-Doh to hang your stuff: it’s forgiving, it’s weird, and it won’t damage the paint. Just don’t use it in a room that gets hot, like a sun-drenched hallway. Heat makes putty go soft, and gravity is never patient.