My favorite funny part in To Kill a Mockingbird occurs in chapter 6. The kids are watching Mr. Avery, a neighbor as he is just hanging out on the porch:
"Golly, looka yonder." He pointed across the street. At first we saw nothing but a kudzu-covered front porch, but a closer inspection revealed an arc of water descending from the leaves and splashing in the yellow circle of the street light, some ten feet from source to earth, it seemed to us. Jem said Mr. Avery misfigured, Dill said he must drink a gallon a day, and the ensuing contest to determine relative distances and respective prowess only made me feel left out again, as I was untalented in this area.
My students regularly miss this entire passage and I completely enjoy pointing it out to them because it is total early high school humor. It also shows how an author can be funny but almost mask that humor behind formal language. The "closer inspection revea[ing] an arc of water... splashing in the yellow circle of the street light" is an old man peeing off the side of a porch. The boys were obviously impressed by his distance ability. Then, "the ensuing contest to determine relative distances and respective prowess" makes Scout feel left out because she doesn't have an instrument to use in order to participate in the peeing contest that Jem and Dill have as a result.
Another moment of great humor occurs around Christmas time (chapter 9) when Scout begins cussing in an effort to get Atticus to pull her out of school. I can just hear a little girl asking to "pass the damn ham." It makes me chuckle.
In chapter 20, Lee uses the revelation that Mr. Dolphus Raymond actually drinks coke in the bottle and sack he uses to let people think that he's drunk. Here, she uses humor to reveal a truth about human nature. People need explanations for why others do something out of the mainstream of society.
Harper Lee uses these humorous moments to color the storyline even more than it is already. This attracts a variety of readers.