How is the mood of the story appropriate in The Adventures of Huckleberry Finn? Quotations/proof from the book would be appreciated (with like page numbers)
The mood of the novel is, for the most part, light and comic. Humor and whimsy define the book more-so than any other element relating to mood. This mood serves to match the genre the novel adheres to, that of the "adventure".
Adventures, satirized famously by Miguel Cervantes (Don Quixote), feature episodic narratives, placing the protagonist or other characters in peril, posing problems to be solved and solving them through valor, wit, or luck. (This is a general description of the genre and not intended to be exhaustive.)
In the case of Mark Twain's adventure, a light mood is appropriate for the adventures of Huck Finn, who solves the many problems he faces through a talent for lies, dissimulation, and wit.
As a work of literature, the novel's purpose has been described this way:
...to entertain them with an amusing, picaresque tale that touches upon timeless subjects such as freedom as seen through the eyes of a highly particularized character.
Seeking to entertain, as opposed to truly challenge social mores, it is natural that a book would take a light tone when it features a series of ridiculous and semi-ridiculous episodes with a run away boy standing at the center.
Taking the analysis one step further, we might agree with the many critics who see the novel as a satire or burlesque. Given this reading, a light and comic tone is not surprising.
In fact, the last third of the book descends into burlesque, according to the novel's critics, as Tom's outlandish schemes to free Jim take center stage.
Identifying examples of humor in the text will not be difficult. Also, the use of humor to create atmosphere and mood is a repeated occurrence in the book, from the scene where Pap Finn sneaks into Huck's room at the widow's house to the revelation that "Tom" is actually Huck and "Sid" is actually Tom.