The events start in August 1887 and apparently take place in the following weeks or, at most, months. However, Mycroft Holmes tells Queen Victoria that Kaiser Wilhelm II had Count Zeppelin working on dirigibles that could drop bombs on Buckingham Palace. Wilhelm II did not become Kaiser until 15 June 1888, and Zeppelin did not start constructing rigid airships until the 1890s.
Dr.Watson says at the beginning of the movie that this takes place in 1887. However, he shows Holmes a copy of the Strand Magazine with "The Red Headed League", which was not published until 1891. Also, the Russian opera singer later tells Holmes that she read about his adventure, "The Hound of the Baskervilles", but that was not published until 1901.
When Holmes and Watson are visiting Mycroft in the Diogenes Club, Holmes mentions the Club's supposed quest to find the Abominable Snowman. The term "Abominable Snowman" wasn't coined until a journalist did so in 1921, many years after our story.
The film's prologue depicts two contemporary men opening Dr. Watson's case and handling the various contents archived inside. We see one close-up shot of a man handling a single pair of old handcuffs and putting them down on the table. A short time later, the filmmakers repeat the very same footage of the man handling the handcuffs and putting them down on the table.
There are references to HMS Jonah undergoing sea trials in the Moray Firth from her base in Loch Ness. The only link between Loch Ness and the sea is the River Ness which is broad and shallow and would not allow the passage of a submarine.