If you’ve been off the Internet for the last two days or haven’t been watching TV, then you might have missed the inappropriate joke made by a 62 year-old man about a underage minor (a point made by Palin in response to Letterman’s jokes):

The “Late Show” host also took a shot Palin’s daughter, while poking fun at the Yankees’ third baseman.
“One awkward moment for Sarah Palin at the Yankee game,” Letterman said, “during the seventh inning, her daughter was knocked up by Alex Rodriguez.”

Letter man followed that joke with another one on Tuesday:

Letterman followed up on the line Tuesday night, joking that “the toughest part of her visit was keeping [former New York Gov.] Eliot Spitzer away from her daughter.”

In effect calling a 14-year-old girl a prostitute.
Palin responded(what mother wouldn’t lash out at an old man making jokes about her underage daughter):

“Laughter incited by sexually perverted comments made by a 62-year-old male celebrity aimed at a 14-year-old girl is not only disgusting, but it reminds us some Hollywood/N.Y. entertainers have a long way to go in understanding what the rest of America understands — that acceptance of inappropriate sexual comments about an underage girl, who could be anyone’s daughter, contributes to the atrociously high rate of sexual exploitation of minors by older men who use and abuse others.”

Kudos to Politico for the whole quote, btw. I was going to use a shortened one from the Daily News but the full quote is much more powerful.
Letterman responded with the blond response,he was too clueless to realize that Willow was the only daughter in attendance:

But Letterman insisted on his show Wednesday night that he was referring to 18-year-old Bristol Palin, who recently gave birth to a son after roiling the presidential campaign with the revelation she was pregnant.
[…]
“These are not jokes made about her 14-year-old daughter. I would never, never make jokes about raping or having sex of any description with a 14-year-old girl,” he added.
“Am I guilty of poor taste? Yes. Did I suggest that it was okay for her 14-year-old daughter to be having promiscuous sex? No,” Letterman said.

Shouldn’t a plugged in talk show host know what he’s talking about? If he knew that a daughter was attending, wouldn’t he know the name of the daughter? Wouldn’t that have been in the story that he or his writers read in preparation of the joke? Of is he getting senile in his old age and forgot the detail? Or is it his bitterness towards Palin blind him to inappropriate nature of the jokes he was telling about a 14-year-old.
I think the bottom here is that Letterman hates Palin so much that he’d use her daughters to ridicule her, not caring about how he’d be perceived. As a dirty old man talking about sex with an underage girl. This begs the question, why does he hate Palin with this much intensity? That he would make such misogynistic comments about her underage daughter having sex and calling Palin herself slutty:

While reading his top ten list Monday night, “Late Show” host David Letterman said Gov. Sarah Palin bought makeup from Bloomingdale’s to update her “slutty flight attendant” look.

Clearly Letterman is thinking about Palin and her daughter(s?) in a sexual way, he might want to repent to his wife about his Palin related fantasy life.
Update: I just had another thought. Maybe the sexual focus of his comments is the easiest way to demean a Christian female politician. He can’t stand her so he wants to use the easiest why to belittle her and ridicule her so that she continues to be the laughingstock of American politics. I think this one backfires on him because the fact that he let his bitterness and hatred push him into inappropriate comments about a minor.