When Victoria takes her household and family to visit the Karim Family in their cottage at Osborne, the Queen introduces her granddaughter Sophie as the Queen of Greece. Sophie did not become Queen of Greece until 1913.
Victoria said she was ruler of "nearly a billion people". The English language adopted this Americanism for 1000 million only in the 1990s.
At the start we hear a call to prayer (adhan) with a loudspeaker which did not yet exist in 1887.
When Victoria and Abdul were riding in a carriage, it starts to snow, despite the fact that all the trees were still in full leaf. In the next shot, all the trees are bare.
Victoria said she was "Morbidly Obese". That term was not coined until the 1990s.
Abdul at least twice refers to his home province as "Uttar Pradesh". That name was coined in 1950, in the respective period the area was known as "United Provinces".
In the beginning, when Abdul is called in the governor's office, a world map hanging on the wall behind the desk is visible, depicting the territories of the British Empire. The map is actually from 1915 and doesn't reflect the empire's territorial extent in 1887, when the scene takes place in the movie.
At the first dinner, we can see the servers holding trays of soup standing behind the diners. Then the boy runs to the kitchen to announce they want the soup course. We see the waiters bringing trays of soup into the dining room then they cut to that same scene of the waiters standing behind the diners with the same trays of soup.
Queen Victoria was told, "But mangoes only grow in India". Actually, mangoes grow in all tropical and subtropical countries.
When Victoria died, her oldest grandchild, The Kaiser, was wearing a German uniform. In those days he and most all royals went to great lengths to dress in honorary uniforms of the host country. He would have been in civilian clothes or a British uniform.