"So what I want to know is this. How often do all these hairy-faced men wash their faces?”
Mr. Twit is introduced as an untrustworthy character, partly due to his long beard. Here, the narrator suggests that some men's beards are not cleaned very often, which is a fitting place to introduce Mr. Twit as his beard is incredibly dirty.
"A person who has good thoughts cannot ever be ugly. You can have a wonky nose and a crooked mouth and a double chin and stick-out teeth, but if you have good thoughts it will shine out of your face like sunbeams and you will always look lovely."
This is a frequently quoted passage from The Twits, as it is very poignant. Roald Dahl is suggesting that a person is only ugly if they have ugly thoughts. If a person is kind and friendly, they can never be ugly because their good thoughts will "shine out of your face like sunbeams."