I think the distrust of confidence men is that its a lie. They have an ulterior motive and are willing to say whatever you will respond to.

With politeness, ideally there is no lie. It's not a polite surface--its a core personality trait. As he described, you may be polite to people you dislike but that's because you know you may simply be having a bad day so no sense in taking it out on a person, or pushing aside a budding relationship. That's really the story of his wife: he was polite, thus he left the door open to meet her again and not sour her impression of him by reacting rudely.

He gives the lie to himself by (almost compulsively!) categorizing his 'marks' as impolite when he feels that they've failed to realize or follow the same rules that he understands so well. It's well and good that he's willing to give people the benefit of the doubt if they're having a bad day, but being unable to relate his coworker's compliment without also noting that it is, in fact, the mark of an impolite person demonstrates that, at core, he doesn't hold her in particularly high esteem. So what's the point of being polite?

Personal growth through empathy.

As in the example of the jeweler, the author's politeness caused the woman to reveal information about herself. And as he states later in the article, he actually enjoyed learning about her work. He now understands this person's perspective a bit better.

I would be interested to know how he has handled conversations with similarly polite people. Did they arrive at a common ground, resulting in a profoundly enlightening conversation, or did they end up in a sort of politeness stalemate, with neither party wanting to disclose information about themselves?

Except his coworker didn't offer a complement. His coworker offered an admission that what she thought was a personality flaw ended up working out. It was, in fact, a rather impolite and off-putting delivery. I see no problem with his description of his coworker as being impolite. The important bit about that interaction was that, because he was a polite person, he didn't immediately treat the impolite remark as being off-putting or insulting or any other way that another not-so-polite person might take it, but he understood that this was just his coworker's way of offering a complement, and that he should take it as a complement despite the delivery.

In other words, a polite person forgives other people for inadvertent impoliteness and recognizes the intent behind the words.

The point is to allow people to get along, get to know each other, and profit from each other's company, despite our human failings. We all have things we'd like to hide, moments of weakness, beliefs, distastes and intolerances both logical and otherwise, all of which keep us apart. Politeness is the strategy which allows us to keep all that shit to ourselves, in check, so that we can get along.