Beards
For the narrator, beards symbolize dirtiness and untrustworthiness, and he cannot understand why so many men choose to have beards. He then introduces Mr. Twit, who has a disgusting and ugly beard that is hardly ever washed. Here, his beard symbolizes his inner ugliness and nastiness, as he is not a good person.
Ugliness
For Roald Dahl, ugliness is not to do with physical features or appearance but is instead a manifestation of a person's inner ugliness. He states that Mr. and Mrs. Twit are ugly because they have ugly thoughts, which have made them more and more ugly over time.
Mrs. Twit's eye
Mrs. Twit has a horrible glass eye, which she can take out at any moment. She uses this to play horrible tricks on Mr. Twits, such as putting her eye in the spaghetti.