It's great to find a discussion about this. I had a vague sense that something was ugly about me when I was younger, but never could figure out what it was, and so sometimes though maybe I was mistaken. Like many of you, it was a double mirror that revealed the secret, and even then, it did not happen right away - I really had to look a long time and examine it. I thought at first maybe I just had the mirrors at a bad angle to each other or something.
Mirrors and lenses do play tricks on us in a sense. It's because the human brain, a very powerful organ, likes patterns and it like symmetry, and when we look at an asymmetric face, it generally somehow rounds things out and we just don't notice. At most there might be a vague impression that something's off or the person is just not good looking, but often there isn't even that. I told someone once that my face was asymmetrical, but he still couldn't see it when he looked.
BUT when we look with two mirrors, and see something an image unlike what we've ever seen before and unlike what we're expecting to see, the brain is thrown off. Anything that protruded in one direction now protrudes in the opposite direction, a 180° change. It's quite different, and though it may try, the brain can't cover that up so easily. We can finally see our face for what it is. The joke is that that's what everyone else sees when they look at us anyway, and what seems so strange to us is actually normal to them (and consequently they see THAT as symmetrical). And of course we're seeing this same reversed image when we look at a photograph of ourselves. (Plus, I think when we look at a person in real life, most of our focus is on the the center of the face, the eyes and facial expressions, rather than the whole frame itself. We look at still images differently.) If you wanted to prove to someone else (not that you would) that your face was assymetrical, if photos didn't work, you'd probably best start by having them look at your face reflected in one mirror, which is normal for you but not for them.
Since I broke through this barrier of the brain, I've come to be able to see it looking at one mirror as well, and to see it in other people I face, without any mirrors. My brain's been trained out of its complacency ... and I don't think I'm the better for it. I wonder if good artists can see this more readily than others. How could you draw an accurate portrait if you're just following your brain and not perceiving what's really there?
I could be wrong, but I very seriously doubt that this has any cause as innocent as sleeping on one side or the other. The shape of the face is mostly determined by genetics, and is bone really that malleable? I also think that we'd see it in a lot more people than we do if that were that cause. And for another thing, I notice the exact facial line in my father. It kills me that even if I get surgery to even out my face, if I ever have kids, I'll pass this on to them regardless. The one thing I could do to help them would be to not have any double mirrors set up in the house so they remain in blissful ignorance.