The narrator knows what Peyton Farquhar thinks and how he feels, and is able to go into great detail about Farquhar's hanging. Since the narrator's knowledge is limited to Farquhar, we don't know much about the Union soldiers who execute him. What are they thinking? Do they feel the execution is justified? Do they feel guilty? Who knows? If the narrator let us into the minds of the soldiers, we might have a very different understanding of Farquhar's hanging. Instead, the limited point of view focuses attention on the inner workings of Farquhar's mind as he faces his death.
By the end of the story, the narrator seems both reliable and unreliable – we know that Farquhar is dead, but we also know that he imagined an escape. The narrator keeps that last bit of important information from us till the end. Does this make the narrator more mysterious than unreliable?