How does Maycomb change after the trial?

Maycomb doesn't really change all that much after the trial. The false conviction of an African American male for the crime of rape was all too common in the South at that time. Old habits die hard, and there is no real sense of outrage at the appalling injustice done to Tom Robinson—certainly not outside the Finch family. The ladies of Aunt Alexandra's missionary circle have no compunction about using racial epithets. They are highly indignant at the behavior of the African Americans who work for them. Not surprisingly, these employees have been grumbling about the outcome of the trial, and this disturbs the ladies of the missionary circle.
The ladies' reaction to the trial's outcome is fairly typical of most white people in the town: a certain indifference tinged with a quiet sense of relief that the "natural" order between the races has been preserved. Most people know as well as Atticus that the trial was not really concerned with getting at the truth; it was a way of reenforcing white supremacy. The difference is that for most of Maycomb's townsfolk, that's considered a good thing, and so they go about their business as if nothing has really happened, harboring the exact same prejudices as before.