Tom Sawyer critiques much of American society in this seemingly light-hearted set of adventures. First, he mocks how easily deceived Americans are and how readily a "con man" can trick them. Early in the book, when Tom is punished by being forced to whitewash a fence, he manages to convince other boys to take on the "privilege" of doing his work by pretending it is fun and then denying them the opportunity to help. As the narrator states, commenting on how gullible people are, "in order to make a man or a boy covet a thing, it is only necessary to make the thing difficult to attain."
Second, the book critiques the American educational system, showing the schoolmaster as a petty tyrant "sitting on his throne" and ruling through corporal punishment. The students don't respect the teacher and the teacher doesn't respect them. Twain uses the schoolmaster to criticize the harsh punishments doled out to students during that time period. He also criticizes people entering professions they are not interested in by revealing that the schoolmaster really wanted to become a doctor. Therefore, he is unmotivated to be a teacher, reads an anatomy book in class, and substitutes harsh discipline for real teaching.
Third, Twain critiques institutional religion. For example, he notes that it is ridiculous for children to be rewarded for memorizing Bible verse after Bible verse, which he argues ultimately makes their minds mush without improving their moral characters. To Twain, religion is better enacted in benevolent and generous actions than in memorizing the Bible.
Overall, Twain satirizes adult behavior for often being as childish as children's behavior.
Twain would no doubt criticize how easily people in today's society can be tricked by politicians, criticize some of the problems in the American educational system (though not corporal punishment, as that has gone away), such as people who still go into teaching without a sense of calling, and he would surely go after religious hypocrites who feel they are Christians because they can recite the Bible, but are also treating others in a way that is un-Christian.