Sonya bursts into tears because plastic surgery has turned her into "a hideous monster" when she is, actually, more beautiful than before, to which Harry comments: "Isn't this an episode of 'The Twilight Zone'?" which would be a reference to the episode 'Eye of the Beholder'.
Grace responds to everybody else avoiding the "elephant in the room" by saying she feels like she's in The Twilight Zone and everybody else are pigs and she's the pretty one but everyone else thinks she's ugly and pigs are pretty.
The sequence where they unbandage Leela to reveal the results of her surgery are pretty much shot-for-shot parodying the pivotal sequence in this episode of The Twilight Zone.
