After the Mass of Thanksgiving at St. George's, Windsor for the recovery of the Prince of Wales from an attack of typhoid in 1871, all the royal carriages bear the monogram "VRI" standing for Victoria Regina Imperatrix (Victoria, Queen and Empress). Queen Victoria was not created Empresss of India until 1876, when the "I" was added to the royal monogram.
Benjamin Disraeli is shown being British Prime Minister in 1866. Disraeli did not become Prime Minister until February 27, 1868. Similarly, Sir Henry Ponsonby is shown as being the Queen's Private Secretary before 1866. Ponsonby did not become Queen Victoria's Private Secretary until after the death of Sir Charles Grey, the preceding Private Secretary to the Sovereign, on March 31, 1870.
The scene in Parliament, preceded immediately by the on screen prompt "1867," where the speaker raises the question of the "Disestablishment of the Irish Church" did not happen under the government of Benjamin Disraeli, as depicted, nor did it happen in 1867 at all. Known officially as The Irish Church Act 1869, was an Act of the Parliament of the United Kingdom passed during William Ewart Gladstone's administration, which was after Disraeli's first ministership (which ended on December 1, 1868) and before his second ministership (which began on February 20, 1874).
At Osborne House, Brown is standing on the upper terrace, below the second story grand hall windows, with the Queen's white pony, ready and waiting for the Queen's call to ride. Seen at upper terrace level, he is standing on the horse's right side, as the Queen is walking through the grand hall with her daughters, she notices Brown standing and waiting through the window, and pauses at the window to observe more closely, but now Brown is standing on the horse's left side, which appears closer to the window because of the angle of the shot..
When the Prince of Wales recovers from typhoid, the Queen commands that a Mass of Thanksgiving be held at St. George's Chapel. Queen Victoria was a devout low-church Anglican/Presbyterian in England and Scotland and would have never ordered a mass. In reality, a Church of England Service of Thanksgiving was held at St. Paul's Cathedral.
Disraeli speaks from notes in Parliament and again at the end of the film. The real Disraeli made a point of delivering all of his speeches - including those several hours long or involving complicated statistics - from memory, and he warned younger politicians against using notes as a crutch.
John Brown throughout wears a greenish blue tartan pattern, except when during his dance with the Queen, he wears a red plaid. It is unlikely that a highlander would wear any clan's plaid except his own, even for a royal event.
The goof items below may give away important plot points.
Incorrectly regarded as goofs
When the Prince of Wales is recounting the assassination attempt, and says the gun was a fake, he is clearly boasting and lying to make himself look good, and diminishing the importance of Brown's role and heroism. The Queen reacts and then announces the award she is giving Brown.