What are examples of how Sherlock Holmes uses his keen observation in either "A Scandal in Bohemia" or "The Adventure of the Speckled Band"?
In "A Scandal in Bohemia," the first story in Arthur Conan Doyle's The Adventures of Sherlock Holmes, Sherlock shows off his powers of observation by telling Watson that he's gained weight, he's begun practicing medicine again, he's recently gotten himself very wet, and his servant girl is clumsy. He deduces these things from the smell of iodoform and the marks on Watson's shoes where the clumsy servant girl tried to scrape off the mud.
He receives an unsigned letter and deduces that the writer (who is coming to visit) is a rich German man from Bohemia and will likely wear a mask. When the guest arrives, Sherlock addresses him as "your Majesty," revealing his knowledge that the guest is the future king of Bohemia.
In "The Adventure of the Speckled Band," Holmes also shows his keen powers of observation to his client by lifting the lace on Miss Stoner's sleeve, uncovering bruises from her stepfather's abuse. Tactfully, Holmes does not say how he discerned this.
As Holmes investigates Miss Stoner's bedroom, he discovers that there is a useless ventilator that leads from Miss Stoner's room to the room of Roylott, her stepfather. Later, Holmes tells Watson that he already knew he was going to find this ventilator because Miss Stoner said her sister, Julia, had smelled Roylott's cigar smoke when she slept in this room the night before she died.