I agree with the above post. The episode involving Mrs. Dubose is the last experience Scout and Jem will share as children. Everything after this (particularly the trial) will be observed, felt, and analyzed differently between the two. Scout maintains her innocence, and a major conflict in the later parts of the book will be her attempt to understand why Jem thinks/acts the way he does. Jem, on the other hand, has little time for Scout, and he processes each new development in the trial quite personally.
By ending the first part with the Mrs. Dubose episode, Lee is also introducing an important lesson to the children. Think of it as a last attempt to fortify their defenses before they are forced into situations beyond their years. Prior to this, Atticus often tells Scout to keep her head when times get rough, and Mrs. Dubose seems to be the testing ground before they face the rest of the community. Thus, they have one final instruction in courage and grace before they have to actually practice those values.