What is the point of view in O. Henry's short story "The Last Leaf," and what are the three coincidences in this story?
This story is told in the third person point of view. It is told by a person or entity not involved in the story itself. This is why the narrator uses pronouns such as he, she, and they instead of "I" (first person) or "you" (second person). This third person narration is also objective. The narrator describes the external appearance of things. He does add some background information and bits of tangential wisdom, but he (narrator) does not get into a character's inner thoughts. Also, this particular third person narration is said to be limited. This usually means that the narrator does have access to just one character's thoughts. But in this case, the narrator is completely limited because there is no direct access to a single character's innermost thinking.
One coincidence is how Sue and Johnsy meet. They are from opposite ends of the country: Maine and California. They just happen to meet at a cafe in Greenwich Village. They also happen to have similar interests: art, chicory salad, and bishop sleeves.
Although this was probably O. Henry's intention, within the world of the story, it is fitting and/or coincidental that Johnsy concludes that she will "leave" the world of the living when all of the "leaves" have left the vine.
It is a coincidence that they happen to live next to Old Behrman, a failed painter who has tried for decades to produce a masterpiece. What a case of serendipity (fortunate coincidence) that he lives near them and is presented with the opportunity to paint a masterpiece: the last leaf which keeps Johnsy's spirits alive and leads to her recovery.