I agree with the previous poster. I'd like to add, too, that the ending of the novel brings the reader full circle. Before her first day of school, when her teacher had told her not to let her father read with her anymore because it would cause "damage" to her learning, Scout often spent time with her father and a book. At the novel's end she's also wearing overalls again. Contrary to what many people have said about Scout's development in the novel, I believe that she hasn't transformed fully into a young woman or "lady." If you view the ending as a repetition or revisiting of the beginning of the novel, Atticus' choice of reading material makes sense. The Gray Ghost is one of Dill's books (from the beginning of the novel) that he brought with him on his summer visit, right?
Update: I checked the opening chapter and it looks to me like Dill brings the copy of The Gray Ghost with him from Meridian. Two passages in Chapter 1 make me think this: Scout tell us that "Dill bet Jem The Gray Ghost against two Tom Swifts..." and Dill says to Jem: "I'll swap you The Gray Ghost if you just go up and touch the house."
The author, Harper Lee, has wisely selected The Grey Ghost as the story which Atticus reads to Scout at the conclusion of To Kill a Mockingbird. The title is ironic since the hero of the novel is similar to the ghostly pale Boo Radley. The plot of the novel is likewise akin to the children's earlier beliefs about Boo. The character, Stoner's Boy, was thought to have been a mischievous sort who was falsely accused and chased about--just like Boo. Stoner's Boy also turned out to be innocent of his crimes, and "real nice, too"--also like Boo. Atticus responds by telling Scout, "Most people are, Scout. When you finally see them."
^Thank you very much for this answer about the book being structurally circular. However, do you know on what page at the beginning of the novel Atticus reads her The Grey Ghost? If so can you also put in some quotes? Thank you