Third Person (Limited Omniscient)
While Anne doesn't narrate the story directly, we do get the story mostly through her eyes. That also means we get her blind spots too. A good example of this is when, after seeing Captain Wentworth through the window of Molland's sweetshop, Anne feels "a great inclination to go to the outer door; she wanted to see if it rained," and thinks, "Why was she to suspect herself of another motive?" (19.6). The narrator doesn't jump in and say, "but REALLY she was hoping to get Wentworth's attention," instead letting Anne's version stand on its own without additional comment. And while we do get a few scenes when Anne's not around (like when Captain Wentworth is talking to his sister), most of the time we find out about events only when Anne hears about them.
Although the narrative is mostly in the third person, an unidentified "I" pops up towards the end: after saying that young people who make up their minds to get married will find a way to do it, the narrator says, "This may be bad morality to conclude with, but I believe it to be truth" (24.1). Who is this "I," and why does s/he wait until the end to declare him/herself? Is there something about this particular statement that requires a first person speaker to make sense? Could an omniscient narrator "believe [something] to be truth"?
The appearance of an "I" here also raises the question of perspective in the rest of the novel – if the narrator is an individual "I" rather than a disembodied voice, what is his/her relation to the rest of the characters? It may be tempting to assume this "I" is Jane Austen herself, but it’s entirely possible Austen is just messing with us by using the first person. Is this momentary "I" the key to the novel, a fake-out, or a throwaway? The answer to all these questions is yes – or no, depending on how you read it. (Literature: the least satisfying Magic 8-Ball ever.)