Letterman dealt with his problem pretty head on instead of a Tigeresque dalliance with the media. I must say that it was pretty effective as the embarrassment was fairly short for Letterman as opposed to Woods, who just cant get out of the papers for about a month now. However, if you have been a fan of the show, it shouldn't surprise one that this is how he dealt with the issue. He has used the format for announcing many things...his marriage, his heart issues, etc...
As far as him being honest with is apology. I think he was, however, with a comedian it is going to be harder to tell. Funny people always link in humour to all things...joyous, shameful or mundane. It is probably more important if the former staffers he had affairs with believe it and his wife believe it rather than us.
Honestly, I think it is a fair sentence. He failed miserably at his attempt of black-mail (for which he was not actually charged). Larceny is basically stealing. The grand part is just a indication of relative value of what was stolen. Six months for some pictures gives him good lengthed time out. There was no way he was getting out of it, so I am sure that this was a plea bargain with a guarantee of a lighter sentence in order to put it to rest. I really don't see this guy doing this again and the 180 days to think about it should reinforce that larceny is probably something he isnt good at or wants to get caught at again.
David Letterman is a extremely private individual. He spends a great deal to maintain his privacy. I suspect that the person that was trying to blackmail him thought that David would do anything to keep this quiet and maintain his highly prized privacy.