Ah, I was looking for that during the movie and I think you might be getting it confused with the fact that he was looking in a mirror and the camera was filming the mirror, so everything would be seen in reverse.
I just saw the 6th day today. I also thought he was looking under the wrong eye lid but I agree with compmania, the camera looked into the mirror & it gave the view of the mirror. - -
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I have just watch this part of the movie, and the slip-up is incorrect. He just look in his left eye to find the dot. You just got confused because it was just a mirror shot. You need to watch the movie again.