1. "Spare the rod and spile the child, as the good book says. I'm a-laying up sin and suffering for us both, I know. He's full of the old scratch, but laws-a-me! He's my own dead sister's boy, poor thing, and I ain't got the heart to lash him somehow. Every time I let him off my conscience does hurt me so; and every time I hit him my old heart 'most breaks." Chapter 1
This quote lays out the basis of the relationship between Aunt Polly and Tom. Aunt Polly is torn between disciplining Tom, as her conscience advises, and indulging him, as her warm heart dictates. She is frustrated by the boy, but loves him and feels sorry for him because his mother, her sister, is dead.
The quote also reveals Twain's interest in dialect. He studied the dialect of his Missouri hometown, Hannibal (on which Tom's town of St Petersburg is based) and used the local vocabulary and pronunciations in Tom Sawyer. "The old scratch" is New England and Southern dialect for the devil.
2. "Huckleberry was cordially hated and dreaded by all the mothers of the town because he was idle, and lawless, and vulgar, and bad - and because all their children admired him so, and delighted in his forbidden society, and wished they dared to be like him." Chapter 6
Huckleberry Finn is the symbol of that which is desired and admired by the children in Tom Sawyer - absolute freedom from parental authority. As such, he is feared and hated by the mothers; he is their worst nightmare, having no structure of rules or work. The different attitudes towards Huckleberry reveal the huge chasm between the values of the children and the adults.
3. "She [Aunt Polly] was a subscriber to all the 'Health' periodicals and phrenological frauds; and the solemn ignorance they were inflated with was breath to her nostrils. All the rot they contained about ventilation, and how to go to bed, and how to get up, and what to eat, and what to drink, and how much exercise to take, and what frame of mind to keep oneself in, and what sort of clothing to wear, was all gospel to her, and she never observed that health journals of the current month customarily upset everything they had recommended the month before. She was as simple-hearted and honest as the day was long, and so she was an easy victim. She gathered together her quack periodicals and her quack medicines, and, thus armed with death, went about on her pale horse, metaphorically speaking, with 'hell following after.'" Chapter 12
Twain satirizes medical fads and people's unquestioning belief in each new one, despite the fact that it invariably contradicts the previous fad. He humorously compares Aunt Polly to Death, one of the Four Horsemen of the Apocalypse in the Bible (Revelation Ch. 6). These horsemen are predicted to ride at the apocalypse, bringing death, war, famine and pestilence in their wake. It was no secret at the time that doctors and patent medicines were a common cause of sickness and death.
4. "Oh, they just have a bully time - take ships, and burn them, and get the money and bury it in awful places in their island where there's ghosts and things to watch, it, and kill everybody in the ships - make 'em walk a plank. they don't kill the women - they're too noble. And the women's always beautiful, too." Chapter 13
After he has been rejected by Becky, Tom runs away with Joe Harper and Huck to an island, to become a pirate. Tom gives a romanticized description of the life of a pirate, drawn from romantic fiction. He lacks a realistic understanding of the consequences of stealing money and killing people, despite the fact that he has recently witnessed a real incident of attempted extortion, murder and robbery in the graveyard. He still lacks the maturity to confront either this event or Becky's attitude, preferring to take refuge in fantasy.
5. "As the service proceeded, the clergyman drew such pictures of the graces, the winning ways, and the rare promise of the lost lads, that...