This is a great question, not only because we have some Latin.
First, let me start with the context. Here is the quote:
The band played the national anthem, and we heard the audience rise. Then the bass drum sounded. Mrs. Merriweather, stationed behind her lectern beside the band, said: “Maycomb County Ad Astra Per Aspera.” The bass drum boomed again. “That means,” said Mrs. Merriweather, translating for the rustic elements, “from the mud to the stars.” She added, unnecessarily, it seemed to me, “A pageant.”
Second, yes, there is a serious mistranslation. Mrs. Merriweather translates the the Latin prepositional phrases as "from the mud to the stars." What it actually means is: To the stars through difficulty (or hardships), or we can say: Through hardships to the stars.
Third, a proper translation of the prepositional phrase is very appropriate for Maycomb. The only way they they will become a just and noble community is through hardships. The citizens of Maycomb will have to take a long and hard look at their hearts and actions. If they do, and have the courage to change, then they can "reach the stars."
The fact that Mrs. Merriweather, a religious hypocrite, translates the Latin wrongly does not bode well for Maycomb. In other words, Maycomb won't reach the star without great effort and hardships! But she does hit upon something unwittingly. Maycomb for its prejudice and its treatment of Tom Robinson is in the mud. This might be the significance of the mistranslation.