The Persian Rug
Apart from the business model, the idea of the deliberate mistake in the rug is to demonstrate that the rug maker is human...not divine. This is a charming philosophical point, although in practical terms, anyone observing the weavers would be unlikely to fall into quite that mistake....
How does it apply to photography? Well, if you were to believe the marketers of some editing programs designed to retouch portraits, imperfection is something to be ruthlessly weeded out. Skins are to be smoothed, noses are to be trimmed and straightened, eyes are to be evened up, and teeth are to be whitened. Otherwise the person depicted would be...would be...ummm. Help me out here. I'm trying to say that the person depicted would be the person depicted.
Okay, I am not decrying a little eye-bag removal for those who have indulged the night before - also, removing roaring red eyes is a kind act. You can whiten teeth a little, but beware of trying to do the sort of thing that suburban shopping centre peroxide and laser clinics do. They are fake professionals and are used to pressure-cooking incisors. Do not attempt it at home on your PC.
I guess what I am saying is please do not try to make Konrad Adenauer look like a Disney princess. If people want to see computer-generated androids there are plenty of movies out these days that do that. Leave your portrait sitter some semblance of their real face and skin. They will be happy enough with it when the Adenauer wrinkles eventually do arrive.