Another factor in obvious stuntmen situations is the set lighting. Everything's evenly lit with few heavy shadows. Compare with something like Enterprise, where the stage has more contrast in lighting, and a substitution's easier to fake.
Huh? How long has it been since you've seen TOS? The lighting is full of shadows. The show's director of photography, Jerry Finnerman, was trained by some of the great black-and-white cinematographers of the noir era, and he used a lot of the same techniques, painting with light and shadow in a way few of his contemporaries even knew how to do anymore. He always shot male actors with heavy crosslighting, putting one side of their faces in shadow to bring out the texture (while always frontlighting women and usually using soft focus or diffusion filters). And there was that very noirish trick he used a couple of times where Kirk's eyes were dramatically highlighted in a narrow strip of light with the rest of his face in relative shadow.
Okay, the lighting in engineering in, say, "Space Seed" is more uniformly bright than it was in, say, "The Enemy Within," where it was very shadowy and mysterious. But that's about that specific episode and scene, not a function of the series as a whole. TOS's lighting was remarkably film-noir for a show made in the 1960s, let alone one set centuries in the future.