The broader themes of To Kill a Mockingbird have to do with good and evil. The novel examines how our perception of good people and bad people change as we grow up. The different qualities of good and evil are not necessarily separated or unrelated, nor there are people who are entirely good or evil. Both elements can be found in every single individual.
The one character who understands this is Atticus Finch, who is involved with different themes of the novel and is able to identify it on the people that surround him. He is also involved in the mad/rabid dog incident.
An important theme of the novel is courage, which can be found in characters that show negative (or evil) values such as racism. For instance, Mrs. Dubose is admired by Atticus for being courageous, but at the same time he condemns her racism.
The rabid dog has been said to represent the racism Atticus has to fight in the town, without the help of other white citizens.
Courage is also shown in the incident with the rabid dog as one of the many qualities that Atticus has, and also one of the reasons he is recognized by others as a protector, not only from the rabid dog, but from evil itself.
The rabid dog incident can also be tied with another recurring theme: injustice. The way Tom Robinson is judged is not fair, but Atticus will be there to defend him, even though he doesn't have to do it. Just the way he must eliminate the rabid dog on his own.