Someone in the film made the point that no face is perfectly symmetrical -- there are always differences between the left and right sides.
The fact that the spy's face was perfectly symmetrical indicated that it was some sort of mask or disguise.
Okay, one more movie, please. Vague memory of a movie about a government rocket project. There is a spy within the project.
Someone places a mirror against a man's photograph, so that his face appears symmetrical -- we see the right side of his face, plus the reflected right side of his face...