Great fan writers don’t need a critique, and bad ones can’t usually benefit from it yet. I comment on great fan-written stories. I rarely comment on stories derailed by bad writing; if there are too many mistakes in the first few pages, I just stop reading. It would be pointless to go on, and equally pointless to review. I have the same policy about original fiction.
Crane Hana on critique.
The thing about unsolicited critiques is that they’re almost never helpful. Even most solicited critiques aren’t particularly helpful, because critiquing is a skill (which is why “editor” is a job), and it’s a skill most people don’t have.
Unsolicited critiques in particular tend to run into one or both of two problems. The first is an inability to approach a work on its own terms. This is the “but why didn’t you write it like I wanted you to?” bucket, which includes everything from misunderstanding the genre (“there isn’t enough romance in this political thriller!”) to nitpicking things about the author’s style. Because, yeah, you might personally hate, say, second person narratives and would never write one… but that’s not actually a useful piece of information to an author who’s chosen to write in a second-person style.
The second problem a lot of unsolicited critique falls into is that it’s not actually designed for the author; it’s designed for the critiquer. That is, it’s not intended to help the author get better on his or her own terms, but rather it’s intended (usually unconsciously) to make the critiquer look “knowledgeable” in some way. Either because they’re praise-seeking from the author (“oh thank you for saving me from myself!”) or from third parties. There’s a bit of a muddled line here because most critique is aimed at media consumers, rather than media producers, which means it’s the sort of critique most people are exposed to, which means they don’t know the difference between the two.
Tl;dr, if you don’t know? Then keep it out of the comments at the AO3. (Also see: any other non-professional venue wherein people share their creative works.)