I agree with all of the items in bullgatortail's list aside from one, the item that also appears in your question. Jem certainly may be said to demonstrate courage in the scene involving the lynch mob outside of the jail in Harper Lee's novel To Kill a Mockingbird; however, Scout does not. Jem is very much aware that her father is at risk; he refuses to budge, and the other two children simply follow his lead and stay as well. Scout's reason for staying, aside from following Jem's lead, is her desire to be recognized by Mr. Cunningham, the father of her friend at school. She does not recognize the immediate danger posed by the lynch mob, and her innocence -- not her courage -- is what ultimately causes the mob to disperse.
The narration in the novel is interesting because of such moments of dramatic irony. The adult narrator is aware of something that the child character is not.
Scout is obviously a spunky and fearless young lady, and she proves her courage on many occasions--often without realizing it.
- She stands up to Miss Caroline at school when she defends Walter Cunningham Jr.
- She is also perfectly willing to fight boys (Walter, Cecil and cousin Francis) when necessary.
- She summons the courage to retrieve the gum from the knothole of the tree on the dreaded Radley property.
- She joins Jem and Dill on their vist to the Radley Place the night that Jem loses his pants.
- She accompanies Jem to the very scary Mrs. Dubose's house.
- She helps to save Atticus from the mob at the jail.
- And she walks the once frightening Boo Radley back to his home and onto the porch.