As someone who has literally just submitted three critical essays I know for a fact that they're not supposed to have headings, headings are commonly used in bigger pieces of work like a dissertation. Since this is the introduction of her essay, retelling and summarising is fine at this point but she shouldn't be doing it in the rest of her essay as that's where she should be analysing and close reading the text she has chosen to write about.
Yeah, I thought so. In my essays (I'm still in second year and a distance learner so possibly things are different at Exeter/in final year) headings would not fly.
Also, I think her introduction seems a bit basic? It may be a longer essay so a longer intro which gives her the room to expand, but in no circumstances would I be recounting the plot like she is there. The introduction is, in my experience at least, for introducing the points you're going to cover. Perhaps it's just her wording.
For example:
"The author, Lemony Snicket, is a pseudonym used by Daniel Handler. Handler uses Snicket in order to participate in the same world that the Baudelaires inhabit."
They're just two statements, she doesn't really link them or make a point. Instead she could write:
"Handler's use of the fictional author Snicket allows him to to participate and exist within the fictional narrative to further the sense of immersion and authorial authority."
Or whatever her point is, I don't know, I haven't read A Series of Unfortunate Events, but she needs to indicate where her statements lead to explore them later in the essay. Her level of writing, if that's the final hand-in, is a lot more basic than I'd have thought. I know a lot of tutors in essay subjects such as English have different expectations in regards to structure, what an introduction and conclusion should look like, so maybe my experience is just of one preference but her introduction is more what I'd write if I was writing a book review rather than a critical essay.
Similarly she says:
"This is the opening line...." and then starts the next sentence
"These opening lines..." when she could make it into one point, there's no real continuation or cohesiveness of an idea, such as
"This is the opening line of the first novel in A Series of Unfortunate Events, setting up the readers' expectations for the series....".
It's very thorough, saying it's a series for children with thirteen books and this is the first, but if she's not making a specific point about there being thirteen books, it doesn't need to be there. Of course I'm not expecting any especial analysis in the introduction but she should be indicating what she
will be analysing and exploring, surely? From those first couple of paragraphs, all we know is that the essay is about
A Series of Unfortunate Events.