What are the supernatural elements in the story, "The Canterville Ghost?"

While Oscar Wilde seemingly has created a typical setting and specter for his story, there are irregularities in his ghost story. Oscar Wilde uses his tale to satirize Victorian society and its affectations, as well as British traditions. Wilde also pokes fun at American pragmatism and materialism. 

One distinguishing element of the ghost story present in Wilde's tale is that of the concept of haunting and other supernatural elements. Traditionally, the ghost is usually linked to a place; such is the case with Sir Simon Canterville, who was once the lord and proprietor of Canterville Chase and now haunts it.

As Sir Simon haunts the mansion, he persists in maintaining the blood stain on the carpet despite multiple efforts by the different generations of Cantervilles to remove it. When he discovers the stain, the new proprietor, Mr. Hiram B. Otis, is appalled that such a stain should be allowed on his floor. "It must be removed at once," he declares. The housekeeper tries to explain that this blood stain has been there since the murder of Lady Eleanore in 1575 and is greatly admired by tourists and "others." Further, she informs him that the spot cannot be removed.

"That is all nonsense," cried Washington Otis; "Pinkerton's Champion Stain Remover and Paragon Detergent will clean it up in no time."

In a few moments, the cleaner has, indeed, removed the stain. Later, it is discovered that the ghost restores the stain whenever it has been cleaned.

Another traditional aspect of ghost stories is the frightening appearance of the ghost and his wearing of chains. When the specter shows himself to Mr. Otis in part two, he clearly has a ghostly appearance. 

Right in front of him he [Mr. Otis] saw, in the wan moonlight, an old man of terrible aspect. His eyes were as red burning coals; long grey hair fell over his shoulders in matted coils; his garments, which were of antique cut, were soiled and ragged, and from his wrists and ankles hung heavy manacles and rusty gyves.

Further, in true ghostly fashion, Sir Simon is able to pass through walls. In part two, the ghost passes through a wall when the Otis children awaken after hearing their father talking to the ghost.

[He] hastily adopt[ed] the Fourth Dimension of Space as a means of escape; he vanished through the wainscoting, and the house became quite quiet. (II)

In the end, despite his supernatural powers, the Canterville Ghost fails to frighten the Americans who have moved into his old mansion.