At the end of the film, Moriarty is seen to have fled to Wyoming Territory, USA, where he is tracked down by Holmes and Watson. The film is set the year the Titanic made its maiden voyage, 1912, and Wyoming became a state in 1890.
Even though the Titanic had four funnels only three actually functioned. The last one was fake, built to balance the ship's lines and make it look more impressive. However, this last funnel did serve a function as smokestack for the ship's massive galley. This is why when the Titanic is in shot, smoke can clearly be seen emanating from all four funnels.