I didn't see bifocals mentioned as I read this thread, so here is what we (my son just got an S3 as well) discovered last night. For him, it works very well, all the time (he wears contacts).
For me, sitting in a recliner while testing......I wear no-line bifocals. When you get to the age where you need bifocals, over time you learn to raise your chin and look through the lower part of the lenses as needed, without even thinking about doing it. And with the progressive style (no-line) bifocals, I will adjust my head angle automatically to 'dial in the best focus' depending on the distance I am from what I am seeing.
That said, I could not get smart stay to work at all......until I removed my glasses. Then it worked just great, because I was no longer raising my chin and putting my face at an angle to the phone. I put my glasses back on, but deliberately looked through the upper part of the lenses (which for a nearsighted bifocal wearing person means so blurry you can't read what you are looking at when it is close) and it works great. But when I raise my chin to get the screen in focus, the angle is sufficient that it throws off the face tracking and smart stay is very hit or miss (mostly miss) even in decent lighting.
So it appears to work very well.........except for those of us with bifocals. I wonder if Samsung could find a way to expand the 'cone' of detection to allow for more angle between one's face and the screen to accommodate us?
Regarding the screen dimming part - it appears that the smart stay icon comes up, and if it does NOT think you are looking at the screen, it dims (as a warning I guess) and then cycles through your screen-off delay time setting once more. The eye icon comes up again at the end of that time span, and it if still doesn't think you are looking, then it turns off the display. While testing without my glasses, the screen never dimmed when the eye icon would show up, and it did indeed keep the display lit even with a 15 second setting.