"But when he knows that he is not only worse than all those in the world, but is also guilty before all people, on behalf of all and for all, for all human sins, the world's and each person's, only then will the goal of our unity be achieved. [...] Only then will our hearts be moved to a love that is infinite, universal, and knows no satiety." (4.1.2)
The elder Zosima's notion of universal love is a tough one to grasp because it involves recognizing that you're no better than anyone else, not even equal to anyone else, but "worse than all those in the world." Only when you accept that can you truly love.
"No, I was the cause of it all, I am terribly to blame!" the inconsolable Alyosha repeated in a burst of agonizing shame for his escapade, and even covered his face with his hands in shame. (4.5.46)
Alyosha's outburst of shame is spontaneous but also a bit perplexing, since all he did was tell Ivan and Katerina about their true feelings for one another. To blame himself for their tiff is a bit much, but it goes along with Zosima's notion of love in Quote #1.
"[...] make yourself responsible for all the sins of men [...] by shifting your own laziness and powerlessness onto others, you will end by sharing in Satan's pride and murmuring against God." (6.3.g)
As in Quote #1, Zosima insists on the notion of being personally responsible for everyone else's sins. To do otherwise would be to disrupt the unity of all mankind in the love of God through a kind of Satanic pride.
What this beating on the chest, on that spot, meant, and what he intended to signify by it – so far was a secret that no one else in the world knew, which he had not revealed then even to Alyosha, but for him that secret concealed more than shame, it concealed ruin and suicide, for so he had determined if he were unable to obtain the 3,000 to pay back Katerina Ivanovna and thereby lift from his chest, "from that place on his chest," the shame he carried there, which weighed so heavily on his conscience. (8.3.67)
Dmitri's shame at stealing Katerina's money to entertain another woman is spontaneous and sincere. It suggests that he's not all bad, despite his violent tendencies.
"It's me, me, the cursed one, I am guilty!" she cried in a heartrending howl. (9.3.4)
Grushenka is driven by her love for Dmitri to feel shame for the way she prodded and goaded him into a jealous rage. It's only when she feels love that she is capable of feeling remorse.
And he also feels a tenderness such as he has never known before urging up in his heart, he wants to weep, he wants to do something for them all, so that the wee one will no longer cry. [...] And his whole heart blazed up and turned toward some sort of light, and he wanted to live and live. (9.8.45)
After being arrested for a crime he didn't commit, Dmitri has a vision that opens him up to love for all mankind, even these fictional peasants in his dream. This vision of love emerges from the seeds of shame we saw in Quote #4 above.
Oh, perhaps this strained love would have grown into real love, perhaps Katya wished for nothing else, but Mitya insulted her to the depths of her soul with his betrayal, and her soul did not forgive [...] naturally, as soon as she had spoken it out, the tension broke, and shame overwhelmed her. Hysterics began again. (12.5.47)
Katerina doesn't recognize how her betrayal of Dmitri at his trial stems from her wounded pride that he left her for another woman. When she finally realizes this, in this quote, she is overwhelmed with shame. The benefit of this is that she gains a greater knowledge of herself.
"I alone am guilty!" Never before had Katya made such confessions to Alyosha, and he felt that she had then reached precisely that degree of unbearable suffering when a proud heart painfully shatters its own pride and falls, overcome by grief. (Epilogue.1.5)
Along with the greater insight she gains into herself (see Quote #7 above), Katerina also loses her overbearing pride when she experiences guilt over her actions.
"[...] still you are guilty of everything, sir, because you knew about the murder, and you told me to kill him, sir, and knowing everything, you left. Therefore I want to prove it to your face tonight that in all this the chief murderer is you alone, sir, and I'm just not the real chief one, though I did kill him. It's you who are the most lawful murderer!" (11.8.93)
Smerdyakov's assertion here that Ivan is responsible for Fyodor's murder is a twisted version of Zosima's belief that we are guilty for everyone's sins. Here Smerdyakov is refusing to take responsibility for the murder and putting all the blame on Ivan.
[...] from the very first moments of the trial a certain peculiar characteristic of this "case" stood out clearly and was noticed by everyone – namely, the remarkable strength of the prosecution as compared with the means available to the defense [...] the debate would take place only for the sake of form, and that the criminal was guilty, clearly guilty, utterly guilty. (12.2.1)
The narrator's ironic tone comes through even in translation with the repetition of the word "guilty." Saying guilty three times suggests that the narrator just isn't sure, so he has to keep repeating himself. The state's version of guilt (determined by a trial by jury) is shown to be flawed: the actual murderer, Smerdyakov, goes free while Dmitri is condemned.