How does the novel illustrate the main features of realism?

Well, you're astute in noting that in many elements of his work, the Duke and King being a perfect example, Twain shows a tendency to integrate his interests in more genres than what is termed "realism." He was a satirist and often a highly symbolist writer, and there are elements of Huck Finn that show these interests. But overall, the idea of realism as a literary genre is to present society as it actually is, and not as a romanticized version of itself. Additionally, realism shows an extra emphasis on psychology, and how a person's psychology changes through social and personal influences. Huck Finn definitely shows these elements for the most part - a protagonist who confronts the ethical dilemma of slavery throughout the novel, battling his psychological contradictions all the while, and with much of his adventure being small moments. That is, the novel is not made of romantic non-stop adventures, but instead much of it is simple talk between Jim and Huck on the raft. But of course, Twain would probably have laughed at the idea that his work fit into a "movement" like realism, and insisted that he just wrote the book. So these imperfections are in some ways the novel's strength. Lastly, perhaps one could argue that the Duke and King, as itinerant con-men, are not so "unrealistic" as they might seem to us today. These type of swindlers did exist, even if Twain overplays it a bit for entertainment and comic value.