Queen Victoria is shown being escorted by soldiers from the Scots Guards. Since 1788, the British Sovereign's official bodyguard has been the Life Guards. In Scotland in 1879, Queen Victoria would have been escorted by the 2nd Troop (Scots), 2nd Regiment of Life Guards.
(at around 10 mins) When the Doctor is examining the telescope, you can see Sir Robert's mark on the floor under the actor's feet.
It is *extremely* unlikely that armed soldiers on guard over the room holding some precious object, told to "defend it with your lives", would accept any food or drink from a person unknown to them without approval from a superior officer.
When Queen Victoria says that her late husband Prince Albert was from Saxe-Coburg, The Doctor whispers to Rose: "That's Bavaria". Actually Saxe-Coburg is located in Thuringia, though next to Bavaria. In addition he implies that Hemophilia is only contracted by inheritance when that is not true.
At dinner, Captain Reynolds speculates that the disappearances of local children have been blamed on wolves. Wolves had been extinct in the British Isles for more than a century by 1879.
The Doctor introduces Queen Victoria to Rose, by saying something like "Rose, I present Her Majesty Queen Victoria, Empress of India" etc. In reality, etiquette says the junior/lower ranked person is presented to the senior/higher ranked person. so the Doctor should have said "Your Majesty, may I present Miss Rose Tyler" or similar.