I know that the noun "correction" is both countable, meaning a change that makes something more accurate than it was before, and uncountable, meaning the act or process of correcting something. When I want to say, "Any correction is appreciated," should I say "any corrections', or are they both correct? Here, I'm referring to my correcting a friend's essay.
Yes, both are correct.
That's because the word any can refer to one or more things i.e. singular and plural.
any - One, some, every or all without specification.
This said, any correction would mean one time/single correction and making it plural means more than one corrections.
They are interchangeable unless you are peculiar about the number of correction/s.