The City on the Edge of Forever is one of the most beloved episodes of Star Trek. Its emphasis on character drama allowed it to move beyond normal viewer's interest and into the mainstream consciousness.
There is a single science fiction conceit in the entire episode: The Guardian of Forever. This time portal is used as merely the springboard for dealing with a character story with a great depth of feeling. One I feel may be almost too ambitious for an hour long television show.
Kirk must enter the time portal to repair errors to history created by a crazy drugged up doctor McCoy. (The Doctor accidentally injecting himself is a thrilling Trek teaser if there ever was one.) The plot follows that in order for history to be restored, Kirk must allow the death of a woman he has unfortunately fell in love with.
The ill-fated romance is a fantastic concept for drama, however the time it is afforded in this episode to be introduced, come to fruition, and act as a dramatic payoff is severely limited. Much of the relationship is relegated to informational dialogue ("I'm in love with Edith Keeler") rather than being narratively shown.
While the climatic payoff is ultimately successful, one could imagine a more effective third act in which everything was earned by naturally unfolding introduction in the prior two acts. This led to a particularly annoying contrivance in the personality of the Edith Keeler character. She is given a penchant for astonishingly accurate insight regard the future our lead character's come from.
I can understand the desire on behalf of the writers to create reasons the characters would be attracted to each other, but this one feels too explicitly convenient. Especially considering that her character is strong enough to survive without this invention. Her optimism alone (which is rooted in the plot via her importance to future history) would be more than enough to attract the attention of our dear Captain. Doubly so when cast against the bleak backdrop of the depression.
Again, this is all a byproduct of having more narrative needs than a single hour can adequately support. It is only natural that the slack be cut in one place or other. It's a great episode when the only sin it commits is over ambition.