Where does it show that the narrator is an unreliable narrator in the text?
The term "unreliable narrator" refers to a narrator who is disturbed or too sujective to be completely credible. This narrator's recount of events is so distorted that it departs from the true understanding of these events shared between the reader and the implied author. However, the term does not necessarily mean that the narrator is a liar or morally untrustworthy.
So, while Gilman's narrator is unreliable since she is obviously mentally disturbed, her narration presents an accurate report of her breakdown as the reader witnesses her deterioration in the story. Also, her recounts of what her husband and her sister-in-law say and do at the beginning of the story when she is fairly well, lend credibility to her reports of their treatment later in the story.
I think that anytime a first person narrator is used there is an element of unreliability. As mentioned above, the narrator may certainly be credible; however, everyone perceives objective truths differently. Even if the narrator in "The Yellow Wallpaper" is correctly relaying events as she knows them, how can we be certain that she is relaying all that has happened? What is left unsaid?