The song "Class" in Chicago, sung by Velma and the Matron, decries the degradation of society's values while being chock full of swearing, insults, and references to bodily functions. The characters singing it are a murderess and a corrupt prison warden no less.
And they follow up the song with reading a fellow inmates private diary.
In Trial By Jury, the Usher instructs the Jury on the "stern judicial frame of mind" necessary for conducting an impartial trial:
Oh, listen to the plaintiff's case: Observe the features of her face - The broken-hearted bride. Condole with her distress of mind: From bias free of every kind This trial must be tried! ... And when amid the plaintiff's shrieks The ruffianly defendant speaks Upon the other side; What he may say you needn't mind- From bias free of every kind This trial must be tried!
For that matter, the Learned Judge declares himself "ready to try this breach of promise of marriage" immediately after gloating that he owed his successful career to committing a Breach of Promise of Marriage.
If you give me your attention, I will tell you what I am: I'm a genuine philanthropist, all other kinds are sham. Each little fault of temper and each social defect In my erring fellow-creatures, I endeavour to correct. To all their little weaknesses I open people's eyes; And little plans to snub the self-sufficient I devise; I love my fellow creatures, I do all the good I can ; Yet ev'rybody says I'm such a disagreeable man! And I can't think why!
The Yeomen of the Guard contains a great double example of hypocrisy used for humor in its Act I finale, where Sergeant Meryll and his daughter Phoebe hatched a scheme to break Colonel Fairfax out of prison. To keep up their facade of innocence, both of them have lines about how shocked they are that the Colonel has gone missing from his prison cell:
Meryll: The prisoner gone, I'm all agape Who could have helped him to escape? Phoebe: Indeed I can't imagine who I've no idea at all, have you?
The bigoted Senator Rawkins in Finian's Rainbow grumbles that his family has had trouble with immigrants ever since they came to America, and also says that he's been so busy defending the United States Constitution that he hasn't the time to read it.
Shakespeare practically owns this trope, as it accounts for most of the ironic humor in his plays.
The tragedy Hamlet gives us the famous line "Brevity is the soul of wit" which is spoken by Polonius... as he rambles on and on and on just to hear himself talk.
In fact, Polonius's entire speech is an example of this trope, with virtually every bit of fatherly advice being something he himself fails at. Hamlet calls him on this multiple times in his bizarre doubletalk.
In The Merchant of Venice, this is a running gag, with Launcelot Gobbo saying things like "To be brief", "Tears exhibit my tongue", and "I have ne'er a tongue in my head"...only to go off on an extended ramble each time. Solanio is also guilty, following the common Shakespeare gag of failing to get to the point:
Solanio: But it is true, without any slips of prolixity, or crossing the plain highway of talk, that the good Antonio, the honest Antonio—oh, that I had a word good enough to keep his name company...
In Romeo and Juliet, when Romeo offers the Nurse money for being a go-between, her line is "Nay, sir; not a penny." Many stagings have her take the proffered money as she says this.
Similarly to the examples under Hamlet and The Merchant of Venice, Friar Lawrence says that he will be brief in the play's final scene, before saying one of the play's longer monologues to recap most of what happened over the course of the play.
In Much Ado About Nothing, Benedick goes on a lengthy rant about how much he utterly hates men who swear they will never marry and then go get engaged. It is the most despicable thing known to man, will he never see a bachelor of three-score again? Women are the most annoying things on the planet and-WHAT DO YOU MEAN BEATRICE IS IN LOVE WITH ME? I SHALL BEGIN COURTING HER AT ONCE.
This is the trope on which run most of Molière's plays, so much so that "Tartuffe" has become another word for "hypocrite" in French.
Knickerbocker Holiday makes a Running Gag out of the corruption and hypocrisy of politicians, but Stuyvesant in his New Era Speech is particularly blatant about it. He denounces the council as the most "preposterous, muddle-headed, asinine, crooked, double-dealing, venal, vicious, fat-headed group of men" ever in charge of a country, then immediately pauses to politely shake hands with one council member. At the end, he tells the people of New Amsterdam they will be consulted in all future political decisions, then dismisses them to talk with the council.
Lampshaded in the 2012 all-female Chalmersspex, a rich businessman's daughter, Cristal Hilton, wants to invest in an invention, and can make the choice between the cinematoscope (made by the Brothers Lumiére) or the kinetoscope (Thomas Edison). (To all the historians currently grinding their teeth — remember, artistic license and Rule of Funny.) Since her sister is on good terms with the Lumiére brothers, she invests in the cinematoscope. Then, when she and her sister wind up on bad terms, she shifts sides to the kinetoscope out of spite — then, when they make up again, she promises to invest in the cinematoscope.
Cristal: Oh, and, yeah, Tommy-boy...I just wanted to say I'm investing in the cinematoscope after all.
Cristal: No hard feelings, right?
Edison: Ms. Hilton, I must protest—to shift sides like that is unethical, it's immoral, it's very, very dishonest!
Cristal: Yeah, but, like—I shifted to your side before, didn't I?
Edison: That was different! That was to my advantage!
In the second act of Waiting for Godot, Vladimir tells Estragon that they should just stop talking and act...and spends the next page repeating this instruction.
If/Then has a pregnant Liz respond to a comment about pregnancy making women overemotional:
Liz: I'm not emotional. Fuck you, I'll kill you.
Malet, une conspiration sous l'Empire features a scene where Captain Steenhower stands guard in the office of General Hullin, presumed dead after Malet shot him. When Mme Hullin cries at the sight of her husband lying in a pool of blood and begs Steenhower to send for a doctor, he remains unflappable, saying that it goes against his orders and she shouldn't be so upset over it; but when a soldier lets out a curse word at the sight of the nearly dead General and his wife, lying unconscious on the ground, Steenhower explodes:
Steenhower: How can you swear in that place and at that time? You see a general drowning in his blood, his wife unconscious, and you swear! You are heartless. You’ll be detained for eight days!
In the musical Golden Boy, one number begins with the singers admonishing each other about the dangers of drinking and cigarette smoking, followed by the Title Drop: "Gimme some."
In The Rivals, Mrs. Malaprop has a speech about the best standards of female education that's full of her characteristic errors, and concludes by saying that the most important goal of a woman's education is "that she might not mis-spell, and mis-pronounce words so shamefully as girls usually do; and likewise that she might reprehend the true meaning of what she is saying."
In The Drowsy Chaperone, the Man in the Chair complains about interruptions to the show (his phone ringing, the power going out, accidentally putting on the wrong record, etc.). Ironically, he is the cause of most of the interruptions to the show: he will frequently interject where he can between lines and scene changes to explain things, sing along with the record, and will often go as far as to pause the record (and the entire show as a result) to elaborate on the actors playing the characters, give his opinion on a scene, or talk about his life.