In addition to diffusing the mob at the jailhouse, Scout's decision to address Mr. Walter Cunningham in a singular and personal manner leads to another positive result. 

In Chapter 23 not long after Bob Ewell spits in the face of their father, Jem broaches the subject of whether juries are really fit to issue verdicts fairly. He suggests that a judge, not a jury, should have the power to decide sentences in capital cases. Jem thinks Tom's trial was a disgrace. He mutters, "Tom's jury sho' made up its mind in a hurry." But Atticus disagrees,

"No it didn't."...That was the one thing that made me think, well, this may be the shadow of a beginning. That jury took a few hours."

Atticus reveals that there was one holdout who kept insisting that Tom deserved an acquittal. He was one of the men from Old Sarum, a "connection" to the Cunninghams. It turns out that Scout, Jem, and Atticus earned the entire Cunningham family's respect that night outside the jailhouse. So, "on a hunch" Atticus put one of their "connections" on the jury, thinking that perhaps this action would work in his favor. It was a risk, but it almost worked. For the Cunninghams left the jail that one night with "considerable respect for the Finches."

Thanks to the "polite" small talk made by Scout with Walter Cunningham Sr., humanity wins out over animal mentality at the jail that night. Tom Robinson survives the night, and the would-be lynch mob returns home without having fulfilled the murder they had planned. Atticus heroically stands by Tom, and the gang from Old Sarum--who had come to hurt or even kill Atticus if necessary--instead pay their respect to him: first, by obeying Atticus's command to speak softly so as not to awaken Tom; and then by sheepishly walking away after Scout's appeal to their human side. Jem gains new respect in the eyes of his father, and his disobedience probably saves Atticus from injury and Tom from death. Unbeknownst to the entire group of men outside the jail, B. B. Underwood silently watches over the scene with his jug of cherry wine and a loaded shotgun: Underwood is not forced into gunplay, and no one is shot or hurt. It is not until the next morning that "The full meaning of the night's events hit" Scout: Atticus suggests that she step into Mr. Cunningham's shoes before explaining that

"... it took an eight-year-old child to bring 'em to their senses... That proves something--that a gang of wild animals can be stopped, simply because they're still human..."  (Atticus, Chapter 15)