In Part 1 of the story, a third-person limited omniscient point of view is employed. This means that the narrator can only report the thoughts and feelings of one character, and that character is the man about to be hanged. In addition, the narrator is not a participant in the...
In Part 1 of the story, a third-person limited omniscient point of view is employed. This means that the narrator can only report the thoughts and feelings of one character, and that character is the man about to be hanged. In addition, the narrator is not a participant in the events of the story. The narrator describes the actions of the other characters, but he only reports what would be visible to an observer. We learn, of the man about to be hanged, that "He closed his eyes in order to fix his last thoughts upon his wife and children." We learn that he became aware of "a new disturbance," as he listened to the ticking of his watch as it appeared to slow down. The narrator even reports the man's thoughts about how he might "throw off the noose and spring into the stream" if only he could free his hands, and his gratitude that his home "is as yet outside [enemy] lines."
In Part II, the narrator reports a tiny amount of Mrs. Farquhar's feelings, that she "was only too happy" to serve the young gray-clad soldier who showed up at their gate. The narrator also reports on Peyton Farquhar's thoughts and feelings, that he is "ardently devoted to the Southern cause," that he felt his opportunity to distinguish himself would come soon, that he was "at heart a soldier" who believed that "all is fair in [...] war." Therefore, this section is written from a third-person omniscient point of view.
In Part III, the focus returns to Peyton Farquhar's thoughts and feelings alone; however, he does not narrate, himself. The point of view is returns to the third-person limited omniscient. In the end, he imagines the sight of his wife and home, "all bright and beautiful in the morning sunshine."
Because the revelation of Mrs. Farquhar's feeling of happiness at serving the soldier she believes to be Confederate is so minor, and one could argue that her feeling would have been visible to an observer, if you were pressed to choose one point of view to characterize the whole story, third-person limited omniscient would be my suggestion. Certainly, the vast majority of the text focuses on Peyton Farquhar's thoughts and feelings, and seems designed to draw him closer, emotionally, to the reader, which is often why the third-person limited omniscient is deployed. Therefore, it best characterizes the entire story.