Humor is a bit tricky when talking about Arabian Nights.
From the perspective of someone born and raised in the American Midwest, I think part of what makes the tales humorous is that they are told very matter-of-factly. The problem is that dry sort of humor might go right over the heads of some people, leading to a lack of overall understanding of the content of the stories.
The humor is largely based on the humor of women, of the stories they would tell when the men left the room. There is this underlying concept of the women telling the jokes and running the show because Shahrazad is weaving all these stories together and manipulating the king into sparing her life.
The repetition of the tales and stories also breeds familiarity and humor. If enough of the younger generation read Arabian Nights, I am convinced that someone would have made a meme or a vine involving the phrase, “But morning overtook Shahrazad…” because it’s in there so many times. It’s not something you generally notice unless it is being read aloud because we have a tendency to skim right over it to continue the rest of the story. It’s also an element of storytelling, but that’s a whole other thing.
If you find the initial Story of the Hunchback humorous, then chances are you have a decent grasp of the type of humor to expect in Arabian Nights.
The World of the Arabian Nights 