Atticus Finch doesn’t show much vulnerability in To Kill a Mockingbird. He is a very rational, controlled person who rarely lets anything get to him. That’s part of what makes him so appealing in the book. While everybody else is losing their cool and giving in to fear, hatred, and prejudice, Atticus calmly goes about his business, which is always about doing the right thing for the right reasons.
However, there is one scene (in chapter 15) where Atticus shows what it is he fears. This occurs in chapter 15 as an angry mob of white men gathers at the jail where Tom is being held. The fact that Atticus is even there at all is a testament to his courage, but then something happened that he never foresaw—his kids showed up.
When Scout, who is oblivious to the danger inherent in the situation, runs up to Atticus, she expects him to be happy to see her:
I thought he would have a fine surprise, but his face killed my joy. A flash of plain fear was going out of his eyes, but returned when Dill and Jem wriggled into the light.
Atticus’ vulnerability is clearly the fear that something could happen to his children.
As for Tom’s vulnerability, is there ever a time when he isn’t vulnerable in the story? He is in danger from beginning to end.
Boo’s vulnerability is expressed secondhand. Check out the end of chapter 30. Why does Heck Tate want to avoid involving Boo in the investigation of Ewell’s death, even though he believes Boo killed him?