Sherlock kissing Mrs. Hudson on the cheek wasn't scripted. Benedict Cumberbatch had known Una Stubbs since he was very young, and it was his reaction on being able to work with someone who was like a mother to him.
The address used to draw out the murderer of Jennifer Wilson --22 Northumberland Street --was once the Northumberland Hotel, which featured in 'The Hound of the Baskervilles' when Sir Henry Baskerville came to stay in London before going out to Baskerville Hall.
Many scenes took place at night, outdoors, or both, during what turned out to be the coldest winter in Britain for three decades. Martin Freeman recalls standing in ice water once for several hours waiting to get a take done. One morning he fell while getting out of his ride to the set and broke his wrist, requiring that he shoot many of his scenes for the next several weeks with his arm temporarily liberated from its plaster cast. He was luckier than Benedict Cumberbatch, though, whose persistent flu turned out to be life-threatening pneumonia, for which he was hospitalized.
The house portrayed as 221B Baker Street is actually 187 North Gower Street. The physical address of 221B does not exist. The Sherlock Holmes Museum is housed in 237-241 Baker Street.
Although this was the first case of the series, it was the last of the first series to be produced, due to Steven Moffat being busy with the fifth series of Doctor Who (2005).