One of the most important uses of sarcasm is the changing tenor of John the Savage's tone in quoting the words "brave new world" from Shakespeare's The Tempest. When he first gets to the World State, John uses the term with complete sincerity, just as Miranda does in the play. But as he begins to see below the surface of this society, he starts to use the quote sarcastically. For example, one day he is taken on a tour and sees mass groups of identical twins. This so bothers him that he finds himself repeating Miranda's words to himself but twisting them to express his disgust: "Oh brave new world, that has such people in it." His sarcastic use of the words marks his growing disillusion with a state that puts superficial happiness and stability ahead of individualism.

Again, as he is surrounding by masses of identical twins in khaki at his mother's death, he uses the term "brave new world" sarcastically to express not wonder, but horror and dismay.

"Ending is better than ending" is one of my favorite official platitudes from that novel, and it, as with so many, is replete with sarcasm in the form of irony, all directed toward the culture of the reader rather than toward the characters in the novel.

A link to questions and answers about this topic in Brave New World provides some specific answers.  Jamie addressed this a while ago with this answer: 

"From Chapter 3: "Imagine the folly of allowing people to play elaborate games which do nothing whatever to increase consumption. It’s madness. Nowadays the Controllers won’t approve of any new game unless it can be shown that it requires at least as much apparatus as the most complicated of existing games." This quote encompasses all three of your criteria: humor, sarcasm, and mockery. It's meaning is that if we don't consume, the government doesn't improve and the society doesn't "win." (Sound familiar in this post 9/11 world??)

From Chapter 17: "Christianity without tears— that’s what soma is." This is an example of mockery. Huxley does not believe that religion should be without some sadness and guilt. "Soma" removes these uncomfortable feelings, making religion watered down and unreal."

Follow the Brave New World links for more information.