Accidental Innuendo: "and [Jim] would always call me honey, and pet me and do everything he could think of for me, and how good he always was."
Angst? What Angst?: Huck's reaction to finding out his father and Miss Watson had died a while ago was either unmentioned or nonexistent.
Though it's understandable with the former.
Big-Lipped Alligator Moment: At one point, Huck and Jim have a conversation that has nothing whatsoever to do with the rest of the story. (It ends with Jim arguing that French people must not be human because they don't speak English.) This was apparently supposed to be funny to nineteenth-century readers, and some critics have contended that Twain included it as a send-up of the minstrel-show comedy routines popular at the time.
Arguably it is also set up to show that Huck and Jim are Not So Different, since even with his education, Huck still is unable to counter Jim's logical (for what he is told) points.
In at least one adaptation, it's made blatantly clear that Jim is playing Devil's Advocate here to encourage Huck to think more for himself instead of uncritically accepting what other people tell him as fact.
Ending Fatigue: The story comes to a grinding halt once Jim gets locked in the smokehouse - in part because Tom Sawyer, once he finally shows up, seems to be trying to take the book away from Huck.
Everyone Is Jesus in Purgatory: An attempted defiance by the author in his preface, saying anyone attempting to find a plot would be shot. It hasn't stopped generations of scholars from analyzing the heck out of this book.
Fair for Its Day: It's now considered by some to be racist, but is actually a satirical work condemning slavery. Also, we have to understand that back then it was considered highly offensive for a southerner to denounce his society in this way. People cry racism for the outdated terms (n-word being commonly used, whether intended badly or not) but it was radical then. And while Jim is portrayed as being ignorant (being Black at that time, he had not received any sort of formal education; Huck has a hard time explaining how it is that French people don't speak English) he is by no means stupid. In fact, he's generally the smartest guy in the room.
Genius Bonus: Prior to the American Civil War, the United States did not have a unified money supply. As such, cash printed in big cities was more easier to pay with. On his journey, Huck has to pay a person in cash for a favor. It is accepted without a hitch because the cash was printed in New Orleans, and New Orleans is described as having some of the most reliable currency available. Not a strong case of Did Do The Research because Twain knew this tidbit first hand.
Misaimed Fandom: Inverted. Sometimes condemned as an unironic endorsement of Civil War-era racism due to its extremely liberal use of the N-word and its somewhat stereotypical portrayal of Jim, despite the fact that the book's primary message is to criticize slavery as inhumane, and that Jim actually subverts many of the contemporary Uncle Tomfoolery stereotypes. Tellingly of the book's true intent, Huck, believing that even God is prejudiced against his black friend, renounces all hope of Heaven for The Power of Friendship.
One-Scene Wonder: The book has quite a few memorable characters who only appear very briefly, but the best example of this has to be Colonel Sherburn, who gives a spectacular "The Reason You Suck" Speechto an angry mob, and despite being a cold-blooded murderer, he remains an impressive figure.
Both unintentionally, as discussed above, and intentionally in regard to Huck's unwillingness to return Jim to slavery. Huck decides to be a Card-Carrying Villain, and most of those around him proclaim themselves good and him evil, but the way it's written makes it clear that they're not good, and he's a morally righteous rebel, or at worst a Noble Demon.
Beatings, whether at school or at home, were quite common, and Huck even states that his back doesn't mind anymore.