The principle use of dialect is the title itself: Wuthering Heights. In the text Brontë tells us that "wuthering" is a word from the local dialect that describes the violent storm weather that blows across the moor:
‘Wuthering’ being a significant provincial adjective, descriptive of the atmospheric tumult to which its station is exposed in stormy weather.'
To reinforce the significance of this word to the story, the narrator, Lockwood, describes the architectural elements designed into the house, Wuthering Heights, to protect it from the storms, a protection the trees and shrubs don't have.
The principal characters are well educated and do not speak in a dialect, though they do use the slang and metonymy of the day and on occassion borrow a word from the locals or from abroad:
‘What the devil is the matter?’ he asked ... [slang]
'I would have set my signet on the biter.’ [metonymy]
' ... you are flurried, Mr. Lockwood ...' [borrowed, 1680 Americanism]
The servants are the ones who dramatically demonstrate local dialects. For instance, Heathcliff's Joseph speaks in heavy dialect: "‘T’ maister’s down i’ t’ fowld. Go round by th’ end o’ t’ laith, if ye went to spake to him.’" Mrs. Dean, Lockwood's housekeeper, is another though lesser example of dialect: "‘Rough as a saw-edge, and hard as whinstone! The less you meddle with him the better.’" Brontë uses dialect to lend authenticity, display temper, create narrative interest, and help create the oppressive mood of the characters and story.