Symbolism, Imagery, Allegory
Not too many folks in The Power and the Glory have pearly white teeth, but there's more than enough rot to go around. The dentist Mr Tench observes death in the "carious mouth" of the priest (1.1.75) and later, in the mouth of the police chief, a "very bad state" that could soon lead to periodontal disease (4.68). The impoverished half-caste (mestizo) has only a couple teeth remaining. We're going to go out on a limb and guess that none of these people have dental insurance.
Like these men's teeth, the world of the novel is falling into decay. The boat on which the priest hopes to escape shows signs of ruin: damaged rail and rotting cords (1.1.4). The policemen who accompany the lieutenant are a disorderly bunch who walk raggedly and sling their rifles anyhow (1.2.1).
The persecution of the Church was meant to create a new and better order, but Greene has no illusions about such idealism. Killing priests hasn't brought an end to poverty. Destroying church buildings hasn't delivered the faithful from their hunger. With decay all around, the people with the power to leave opt to do so. Others, like the family, stay, hoping for a rebirth and renewal. Maybe they should start with flossing.