The man can't stand the old man's eye. It has nothing to do with the elder, he just hates his blue eye. He states, "I think it was his eye! yes, it was this! He had the eye of a vulture—a pale blue eye, with a film over it." This scene is important because he plans on killing the old man to get rid of the eye.
The man finally got rid of the vulture eye. He doesn't have to worry about the blue eye anymore because it's gone. He says,"His eye would trouble me no more." This scene is important because it's the climax of the story.
In this scene the man is confessing because he couldn't stand the noise in his head. “Villains!” I shrieked, “dissemble no more! I admit the deed!—tear up the planks!—here, here!—it is the beating of his hideous heart!” , he cried out. This scene is important because he drives himself crazy to the point where he confesses to the murder.