Atticus uses the term "disease" deliberately. A disease infects and spreads, which is what happens in Maycomb. Good people, kind people, are infected by the disease. The disease spreads throughout the town. Then, suddenly, those kind people are acting against their nature.
Take for example the incident at the courthouse. Having been infected by racism, a mob of men show up to lynch Tom. They are not acting rationally, they are infected with the mob mentality.
Atticus cures them of the disease by calling on their better nature. He asks Mr. Cunningham about Walter specifically, reminding him of what is important and what message he is sending his son.
The cure that breaks up the lynching does not hold up in court, unfortunately. Despite overwhelming proof of Tom's innocence, the town is too infected to act honestly and allows their racism to control their actions in their conviction of Tom.
Some context is in order. In chapter nine, Atticus is talking with his brother, Jack. The trial of Tom Robinson is about to commence. Atticus knows that the trial will be a heated one, filled with emotions, perhaps violence, and no doubt controversial. He also knows that his children will be caught in the crossfire, and they will have to experience some difficult and unpleasant things.
Within this context, Atticus hopes that his children will not become bitter or adopt the racism of Maycomb. This latter point is what Atticus calls Maycomb's disease. More specifically, Atticus knows that the people are Maycomb are reasonable in every other area of life, except when it comes to blacks. He does not have a good explanation for this. Here is what he says to his brother:
...I hope and pray I can get Jem and Scout through it without bitterness, and most of all, without catching Maycomb’s usual disease. Why reasonable people go stark raving mad when anything involving a Negro comes up, is something I don’t pretend to understand... I just hope that Jem and Scout come to me for their answers instead of listening to the town. I hope they trust me enough... Jean Louise?
In conclusion, Maycomb's racism is the disease of which Atticus speaks.