While the "evil twin" trope was already a television cliche by the time "The Enemy Within" came around, the episode put a fresh spin on the idea by having the evil twin actually be the dark side of the personality of the series' lead. The episode is certainly one of the darker-themed entries in the early first season, with effective direction by Leo Penn. Shatner turns in one of the greatest of his performances on the series, compellingly portraying both the "evil" and the "good" Kirk as recognizably distinct and different types. The raw elements of this episode work so well, as they do in the best episodes of TOS, that the viewer overlooks the absurdity of the central premise (that the transporter could seperate positive personality elements from negative ones.) The subplot of the stranded crewmen succeeds in adding tension to the central storyline.
Moment you might miss if you're not paying close attention - when Scotty is discussing the transporter situation, and the inadvisability of bringing the stranded crew aboard, he says "They might all be duplicated like y-" and then quickly catches himself and says "Like the animal." No dummy, Scott has of course figured out the obvious origin of "the imposter".