The overall tone of the first passage in A Scandal in Bohemia is one of mystery, awe and education. The story is the first published in The Strand Magazine (1891) and very probably the introduction of Sherlock to the general public.
The tone of the first passage is mostly mysterious. The reader is taken into the mystery along with Watson, discovering the Bohemian paper origin simultaneously with him (p.5). The shared experience lends an air of suspense to the story. After the King of Bohemia is introduced into the mystery, there is a staccato exchange between him and Holmes (p.9). The rapid-fire exchange builds tension and demonstrates to the reader the speed of Sherlock's thought process.
The passage also lends itself to awe. As Watson enters the rooms at Baker Street, Holmes is immediately able to determine how much weight he has gained since marriage (p.3). He also deduces other facts about Watson's recent adventures. This act is repeated upon the King of Bohemia who tries to hide his identity from Holmes (p.8). The simple deductions give the reader a sense of wonder about his mental prowess and perhaps induces a bit of jealousy.
Finally, the passage includes a hint of education for the reader. Watson questions Holmes on how he was able to accurately provide such detail. Sherlock gives a quick lesson on the deductions (p.3). In retrospect, it seems an easy to replicate parlor trick, but Holmes explains it is much more. Sherlock gives a brief lecture on the importance of not just seeing, but of observing the world (p.4). Observation he explains is understanding the contextual details around you.
The passage is an excellent introduction into the manner of Holmes and his cases. The reader is hooked into the mystery along with the narrator, Watson. There is a sense of awe at the skill of Holmes and a lesson in his methods giving the reader the sense they can replicate the skill.