The opening number, "Mac the Knife," recounts Mac's various crimes. While most of them involve murder and theft, this one reflects his fatal flaw: his lust. The "violation" refers to rape, a horrible crime, which foreshadows Mac's lustful habit of seducing women with trickery.
MRS. PEACHUM. A fine opinion of your daughter you have.
PEACHUM. The worst. The very worst. A lump of sensuality, that's what she is. (1.1.177-179)
When Polly gets married behind her parents' backs, they judge her harshly. From being their daughter, she has transformed into a sexual being which, in the eyes of the Peachums, is "the worst" that could happen. Rather than a human being she's now a "lump"—not exactly flattering.
MATTHEW. And besides, I never use filthy language with her. I respect Kitty too much. But maybe you wouldn't understand that, the way you are. You're a fine one to talk about filth. Do you think Lucy didn't tell me the things you've told her? Compared to that, I'm driven snow. (1.2.146-150)
Mac calls Matthew's girl, Kitty, a "slut," which offends his buddy. He claims to respect her, unlike Mac's attitude toward his women (yes, plural). Matthew understands that language reflects respect or disrespect, while Mac either doesn't understand it, or just disrespects everyone he lusts after.
Want it or not, he can't ignore that call.
Sexual obsession has him in its thrall. (2.4.191-192)
Mrs. Peachum sings about Mac's fatal flaw, his incapacity to resist the hookers. She calls him "sexually obsessed," and that inability to "ignore" the call reminds us of that scene with the sirens in the Odyssey. It's beyond his control.
LUCY. I hear you have a lovely ankle And I'd love to see such a complete tart.
They tell me that Mac says your behind is so provoking.
POLLY. Did he know, did he now?
LUCY. If what I see is true he must be joking. (2.6.145-151)
Inspiring Mac's lust becomes an Olympic event when Polly and Lucy start competing for his attention. Rather than being offended by his lecherous attention, the girls strive for it, comparing behinds and ankles. Mac reduces them to body parts, and sadly they accept their role.
JENNY. And if our friend Suky Tawdry isn't here with us now, it's because he went on from me to her to console her too. (3.7.59-61)
Well, we never. Mac is just a scandal. He busts out of jail and goes straight to Jenny, one prostitute. Then, from her place he moves on to yet another hooker, Suky Tawdry (whose name, by the way, is killer). Mac's seemingly insatiable appetite for women is, in a word, lust.
MRS. PEACHUM. They've put his neck just under where the noose is
And what's he thinking of, the idiot? Floozies. (3.7.75-76)
Mac's weakness for women is stronger than his will to live. Even though he knows that if he sticks around town he'll be captured and hanged, as Mrs. Peachum sings, he's overcome by his desire for ladies of the night and goes for them rather than saving his own skin.
You saw the lovely Cleopatra
You know what she became.
Two emperors slaved to serve her lust.
She whored herself to death and fame
Then rotted down and turned to dust. (3.7.268-272)
This song uses historical figures to provide examples of downfalls, and there's a verse dedicated to precisely our sexy theme: lust. Cleopatra had pretty powerful boyfriends, including not only Julius Caesar but Marc Antony, too. Still, when she was finally defeated (in battle) decided to kill herself. The song blames her lust for her downfall, though it might be harping too much on Cleo.
But one fine day his heart was won.
So now that time is getting late
The world can see what followed on.
His sexual urges brought him to this state—
How fortunate the man with none! (3.7.303-307)
The first line of this verse makes it seem like Mac fell in love: "his heart was won," which led to his ignoring his own safety in order to be with his lover. But skip down a few lines and check out what was really going on: "sexual urges." Sorry, Mac—that's not so romantic and therefore unforgivable, at least in the play.
MATTHEW. excitedly Who was lying around with Suky Tawdry instead of clearing out? Who was lying around with Suky Tawdry, us or you? (3.9.73-75)
Mac wants his fellas to bring him some money to bribe the chief and get his behind out of jail, but they're not really feeling it. Matthew lets his old boss have it, reminding him that his lustful ways got him into this mess in the first place, and that they're not really responsible for cleaning up after him.