These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
In the 2011 film Heathcliff is black, whereas in the book he is just described as "dark" and probably is of some Romani heritage.
Asshole Victim: It's very easy to argue that Heathcliff's successful degradation of his former tormentor Hindley is well-deserved.
Draco in Leather Pants: Many female readers insist that Heathcliff is a dashing hero, despite his many, many shortcomings (even to the point where they thought his digging up Catherine's body was romantic). The author herself makes fun of this sentiment among her readers by making Isabella Linton idolize him. Catherine admonishes Isabella that "He's not a rough diamond—a pearl-containing oyster of a rustic: he's a fierce, pitiless, wolfish man" and Heathcliff comments on Isabella's naivety and romanticism regarding him, mocking it later in the book. It is very amusing that Twilight tries so hard to compare itself to this story, when it is in fact denouncing the kind of relationship Stephenie Meyer tries to glorify.
The famous quote "I am Heathcliff!" is actually very misleading if you just read the back cover. The line from Nelly right after it is: "If I can make any sense of your nonsense, Miss, it only goes to show me that you are ignorant of the duties you undertake in marrying; or else that you are a wicked, unprincipled girl."
External Retcon: There's a sequel to this called simply H, which relates a letter that Heathcliff sent to Catherine; it arrived on her wedding day, but that cruel, meddling Nelly Dean keeps it from its intended recipient. In the end, it relates Heathcliff's true heritage (brace yourself!): He's the son of Edward Rochester and his first wife Bertha! Never mind that no estimation of when Jane Eyre occurs would allow for Rochester and Bertha to have been married in or before 1764, Heathcliff's estimated birth year. Very likely they weren't even born yet themselves.
Hilarious in Hindsight: In complete fairness, given Isabella Linton-Heathcliff's fate, it is difficult to imagine why anyone would constantly compare a book to Wuthering Heights and name the heroine of said book Isabella...
As Heathcliff begins his descent into suicidal madness, Nelly ponders the mysteries of his origins and wonders if he truly might be part goblin, demon, or vampire... but quickly dismisses such theories as "absurd nonsense."
Magnificent Bastard: Heathcliff, who manages to gain ownership of both the Heights and the Grange despite being neither an Earnshaw nor a Linton, or even a member of the gentry, through a combination of seduction (of Isabella and indirectly of Cathy Linton) and manipulation of the legal system.
Misaimed Fandom: Despite Brontė pulling absolutely no punches in her description of Heathcliff, despite Catherine herself stating that he has no hidden depths of love and tenderness, despite Heathcliff's own statement that he hopes Catherine wakes up in torment in the next world for rejecting him...teenage girls will insist on seeing him as a romantic hero!
Who's Your Daddy?: Some readers have debated whether or not Catherine Linton is in fact the biological child of Heathcliff and Catherine, due to the close timing of his return to the Heights and her conception. However the book mentions the strong resemblance between Cathy II and Edgar, making this unlikely.
The bigger question: Is Heathcliff the first Mr. Earnshaw's son?