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.
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.