"Narrative consistency and flow from scene to scene."
As a longtime professional copyeditor, I dispute the definition above.
The copyeditor looks for bad grammar, unclear sentence structure and punctuation, politically incorrect terminology ("sex" instead of "gender"; "he" when it should be "they" or "he or she" or alternating), outdated spellings or word usage ("Web site"), wrongly spelled or capitalized or italicized technical terminology, wrongly abbreviated terms, inconsistent use of terminology or preferred spelling of a term from chapter to chapter (especially if in a text with multiple authors), how dialogues or boxes or sidebars are presented, credited, and punctuated, the numbering of figures and the like, the captioning, and more of the same.
Whether in a work of nonfiction or fiction, the copyeditor does not mess with narrative consistency or flow or make comments on it. Only at a sentence or paragraph level would the copyeditor dispute something presented as fact that is not supported by the text properly (in the sentence structure, by footnotes, etc.) or is--in relatively rare cases--completely unsupported by any scholarship and reading like myth. The copyeditor would not change these out of hand, but would make comments urging a rewrite, most often a rewrite for clarity. If the author's point is made circuitously in the same paragraph or is substantially repeated, the copyeditor would comment on that. Comment, not change. Suggest which sentence to remove, but not remove it.
In fiction, attention would be paid to spelling, correct usages of words to their real definitions (no "disinterested" for "uninterested," no "flaunt" for "flout"), the punctuation of dialogue, to all character or place names remaining consistent throughout, and to the kind of punctuation used. Excessive use of dashes, for instance, would be noted in both nonfiction and fiction, as would any other sentence punctuation that makes the text hard to read. If every sentence starts with "So" or "But," the copyeditor should change it in nonfiction and only suggest changes in fiction or ignore it as a style choice by the author. Similarly, if an author seems to be deliberately using nonstandard capitalization or hyphenation for a term consistently throughout the story, the copyeditor could question it, but should not change it out of hand. However, if a plot makes no sense or a character acts out of character, it's not the copyeditor's job to note that. Dramatic flow from scene to scene also is the business of a different level of editing. Malapropisms, commas where they don't belong, and other technical issues including spelling (even after Spellcheck) are the copyeditor's meat.
The proofreader is the last line of defense for malapropisms and careless spelling corrections ("poured over" for "pored over"; "grizzly" for "grisly") as well as for typos, if these were not caught at the copyediting stage. The proofreader should not change sentence structure or "correct" what the proofreader views as poor writing.
I am well aware that many people hanging out shingles as copyeditors and proofreaders today do not adhere to these standards, but these are what traditional publishing professionals do and have done for decades. There's more, of course. That's why the Chicago Manual of Style is a very long book.