I think the primary advantage of using Scout as the narrator of To Kill a Mockingbird is her innocent and naive understanding of the world around her. Scout rarely editorializes about the reasons thing happen; she tells the story in a down-to-earth and matter-of-fact manner. There are examples where she repeats stories without completely understanding them (Mr. Avery's long distance urnination is one). She has to ask Atticus what rape means, and even after hearing his explanation, she is probably still unclear about its deeper ramifications. When she helps Atticus to quell the lynch party, she has no idea of their true intent. By using this child-like narrative, it allows the reader to speculate and reason about the actions for himself.
This is an interesting question. The only disadvantage that I can see of having Scout as the narrator is that only one perspective is presented. She is not omniscient. Additionally, this is a memory piece, so we have an adult looking back in time and speaking through the voice of a child. This can be problematical because, as time passes, the way that we view events changes. Scout is remembering the past and telling us about the past but with the knowledge ahead of time as to how things work out. This can be a disadvantage because there is a built in narrative bias that colors the reader's perception of events.
As to the advantages of having Scout as the narrator, the firat one that I can think of is the fact that she is so close to the source. She lived the events, so she has an eye-witness perspective. Also, because this story is told through the eyes of a child, there is a truth and honesty in the telling that might not exist if it were told through an adult's view of the world. Children are less jaded, for the most part. They are not molded by society, and they tend to see things in terms of black and white, right and wrong, without societal prejudgements (for instance, Scout sees nothing wrong with being at Calpurnia's church, and she sees everything wring with labeling Tom Robinson as a bad man just because of the color of his skin). At the same time, she also feels the pressure from the adult world when people begin to turn against her because Atticus is defending Tom. She does not understand why the town is turning against them. Yet the simple fact that she does not fully understand makes the narrative even more powerful for, when we look at the world through the eyes of a child, things are often much simpler and clearer.