Odd coincidence: I too was born in 1947; I too have a beard that resembles Dave Letterman's; and I too haven't shaved since sometime in the early 1980s—I have forgotten the exact year. I had a beard intermittently before that, starting when I was a college freshman.

Yes, I think he could trim it a bit better. I agree that shaving one's neck and cheeks is a good idea, especially for a professional performer. He could probably get his makeup person to do it—unless union rules require a professional barber—but surely he, or his network, can afford it.

Another suggestion I have is to trim his mustache a bit shorter, so his mouth isn't hidden. He looks down a lot, at the papers on his desk, or maybe just out of habit, and with his head bent down you can't see his mouth. Although he's usually pretty deadpan, the expressiveness of the lips is an important communication tool. Let us see those lips!

No, I hope he doesn't shave it off completely.