Jack: My dear Algy, you talk exactly as if you were a dentist. It is very vulgar to talk like a dentist when one isn't a dentist. It produces a false impression. (I.73)
It’s the timing of this statement that makes it so funny. Jack’s point seems to be that dentists don’t talk like anyone else. However, Jack has just lied to Algernon about his name, his ignorance of a person named Cecily, Cecily's identity as a vertically-challenged aunt, and why his aunt calls him "uncle." It is not Algernon who is being pretentious or hypocritical; it’s really Jack.
Algernon: To begin with, I dined there on Monday, and once a week is quite enough to dine with one's own relations. In the second place, whenever I do dine there I am always treated as a member of the family, and sent down with either no woman at all, or two. In the third place, I know perfectly well whom she will place me next to, to-night. She will place me next Mary Farquhar, who always flirts with her own husband across the dinner-table. That is not very pleasant. Indeed, it is not even decent... and that sort of thing is enormously on the increase. The amount of women in London who flirt with their own husbands is perfectly scandalous. It looks so bad. It is simply washing one's clean linen in public. (I.92)
Algernon’s protests to dining with his Aunt Augusta are funny because many of us have felt the same way about eating dinner with our families. He complains about how families treat their own family members at dinner—sending them down quite improperly with either "no woman at all, or two"—which is no fun. Algernon is most offended by the fact that the woman he’ll be seated next to flirts with her own husband and nobody else. Algernon’s statement is funny and foolish because he recoils at the very thing that society values.
Lady Bracknell: Well, I must say, Algernon, that I think it is high time that Mr. Bunbury made up his mind whether he was going to live or to die. This shilly-shallying with the question is absurd. Nor do I in any way approve of the modern sympathy with invalids. I consider it morbid. Illness of any kind is hardly a thing to be encouraged in others. Health is the primary duty of life. [...] I should be much obliged if you would ask Mr. Bunbury, from me, to be kind enough not to have a relapse on Saturday, for I rely on you to arrange my music for me. It is my last reception, and one wants something that will encourage conversation, particularly at the end of the season when every one has practically said whatever they had to say... (I.130)
This passage reveals Lady Bracknell’s folly not just in her absolute lack of sympathy for a dying person, but because she talks about life and death as if it were just another choice one could make on a daily basis. She is indignant at Bunbury’s "shilly-shallying" (the Victorian equivalent of flip-flopping) about whether to live or die.
Jack: May I ask you then what you would advise me to do? I need hardly say I would do anything in the world to ensure Gwendolen's happiness.
Lady Bracknell: I would strongly advise you, Mr. Worthing, to try and acquire some relations as soon as possible, and to make a definite effort to produce at any rate one parent, of either sex, before the season is quite over. (I.215-216)
The comedic timing for this line is brilliant. After coming off an emotional roller-coaster ride that ends in a broken heart, Jack is told that the only thing he may do to improve his position is to "produce at any rate one parent, of either sex, before the season is quite over." As an orphan, it's impossible for Jack to find his parents. Secondly, think about the use of the word "produce"; when referring to people, we think of reproduction as having kids. Thus, this line is contradictory both in its use of "produce" and in its implication that Jack’s parentage is a choice.
Algernon: Well, I don't like your clothes. You look perfectly ridiculous in them. Why on earth don't you go up and change? It is perfectly childish to be in deep mourning for a man who is actually staying for a whole week with you in your house as a guest. I call it grotesque. (II.175)
Algernon’s comments on Jack’s clothes are foolish (but funny) because he says they’re hideous and inappropriate for this occasion of happiness. But it is actually Algernon whose arrival foiled Jack’s plan, and make his mourning clothes look "perfectly ridiculous."
Jack: How can you sit there, calmly eating muffins when we are in this horrible trouble, I can't make out. You seem to me to be perfectly heartless.
Algernon: Well, I can't eat muffins in an agitated manner. The butter would probably get on my cuffs. One should always eat muffins quite calmly. It is the only way to eat them.
Jack: I say it's perfectly heartless you're eating muffins at all, under the circumstances.
Algernon: When I am in trouble, eating is the only thing that consoles me. Indeed, when I am in really great trouble, as any one who knows me intimately will tell you, I refuse everything except food and drink. At the present moment I am eating muffins because I am unhappy. Besides, I am particularly fond of muffins. [Rising]
Jack: [Rising] Well, that is no reason why you should eat them all in that greedy way. [Takes muffins from Algernon.]
Algernon: [Offering tea-cake] I wish you would have tea-cake instead. I don't like tea-cake. (II.373-378)
This passage is as close to slapstick comedy as Wilde gets. First of all, it’s hilarious that the men are fighting over muffins when the loves of their lives have just left them. Plus, it’s just silly for grown men to be grabbing muffins from each other; they’re acting like children.
Gwendolen: In matters of grave importance, style, not sincerity is the vital thing. (III.19)
Our common sense tells us that Gwendolen has it backwards. In fact, this is one of the lines that makes us question the title of the play. If "style, not sincerity is the vital thing," then what exactly is the importance of being earnest? This line encapsulates the genius of the play.
Algernon: My dear Aunt Augusta, I mean he [Bunbury] was found out! The doctors found out that Bunbury could not live, that is what I mean—so Bunbury died.
Lady Bracknell: He seems to have had great confidence in the opinion of his physicians. I am glad, however, that he made up his mind at the last to some definite course of action, and acted under proper medical advice. (III.55-56)
Algernon seems to buy into Lady Bracknell’s foolish idea that life and death are a matter of choice. To get rid of Bunbury, Algernon lies that he decided to die when the physicians "found out that [he] could not live." Lady Bracknell continues the hilarity by approving that Bunbury finally "acted under proper medical advice." This shows that one of Wilde’s primary comedic techniques is to turn a serious subject into something lighthearted.
Lady Bracknell: Kindly turn round, sweet child. [Cecily turns completely round.] No, the side view is what I want. [Cecily presents her profile.] Yes, quite as I expected. There are distinct social possibilities in your profile. The two weak points in our age are its want of principle and its want of profile. The chin a little higher, dear. Style largely depends on the way the chin is worn. They are worn very high, just at present. Algernon!
Algernon: Yes, Aunt Augusta!
Lady Bracknell: There are distinct social possibilities in Miss Cardew's profile. (III.73-75)
First of all, Lady Bracknell’s sudden approval of Cecily is based on the young girl's inheritance. We don't think Lady Bracknell is sincere when she compliments Cecily’s beauty. Secondly, it is absurd to divine "distinct social possibilities" from one’s profile.