"The Eye of the Beholder" is the sixth episode of the second season of The Twilight Zone, and was first broadcast in November of 1960. It starred Maxine Stewart and Donna Douglas as patient Janet Tyler. This is one of the Twilight Zone episodes that has reached wide popular knowledge through osmosis, so I will discuss both the plot and the resolution, with spoilers.
Throughout the episode, the doctors and nurses around Janet are shrouded in darkness, and shown only from the rear or in profile. They talk about the hideous deformity that she suffers from, and she is so horrified at her own departure from normal that she wishes to die if the operation doesn't work. When she is finally unveiled, we find out that she is a woman who looks normal by our standards, and then it is revealed that everyone else around her has strange, porcine faces.
Some of the previous Twilight Zone episodes, especially from this season, had interesting set-ups that were spoiled by the conclusion. To me, this episode was the inverse: I found the long scenes of concealed people talking in shadows to be difficult to get through, but the "twist" was, for once, dramatic and surprising. (And this was for someone who has known about the conclusion for years: for its original audience, it must have been even more effective.)
Another point of interest that would only come to someone watching the episodes in order is how this episode contrasts with the previous episode. That episode too had someone imprisoned by an authority figure because they were deemed deviant. However, in that episode the person who takes pity on them is a fool and a sucker, while here we are made to see that the judgement against Janet Tyler is unfair. Although I remembered the basic outline of the episode, it was only after rewatching that I saw there was a political and social message in it as well: the episode takes place in some sort of totalitarian state where being deviant is systematically socially engineered away. I don't know whether Rod Serling meant this as a specific or topical reference, or whether it was just meant to enhance the dystopic atmosphere of the story. In either case, more than just being a story about aesthetics and judgement, this is a story about authority and social norms, and the viewer can make of that what they will.