While Holmes is playing Solitaire and talking to Watson in the train carriage (6:50 mins into Part 2 of the DVD release) the position of the brandy glass on the table, in front of Holmes, changes positions between shots.
When Stanley I. Bullard has a drink with Sherlock Holmes, he holds his glass in his right hand when the camera angle is at his back, but when he is seen from the front, he holds the glass with both hands in his lap.
Near the start of the film Holmes is summoned to attend Buckingham Palace and Beefeaters are seen on guard. However, they only guard the Tower of London.
When Sherlock and Mycroft attend Buckingham Palace at the beginning of the film, there are Yeomen of the Guard on duty, one of whom is clearly female. Apart from the fact that Yeoman are only ever on guard duty at the Tower of London, there were no female Yeomen during the reign of Edward VIII. The first female Yeoman, Moira Cameron, was not appointed until 2007.
The ship name is "St Louis", but the life saver ring says "Queen of Natal".
When Holmes and Watson pursue the two people who look for the treasure hoard, these two say that it will soon be bright day. Clearly, this was shot in daytime and it is already daytime.
Just before the safe is opened a character Saye that "as Governor-General of the Union of South Africa" he is presenting the diamond to King Edward. Edward VII died on 2 May 1910. The Union of South Africa was not formed until 31 May 1910, until that the senior colonial officer was the Governor of the Cape Colony.
Lestrade & Watson talk about Marconi taking a different ship because the maiden voyage of the "brand new Titanic" was delayed. But the Titanic was not launched until a year after the film is set, and not finished for a year after that.
During the Polo Match, which is supposed to be in South Africa, The Round Tower of Windsor Castle (England) can be seen in one shot.
When Holmes sits down at a table in the train the boom mic is clearly brought into view.