When Johnston is about to board a ship to England in 1931, a ticket office window is seen in the background with opening and closing times given in simplified Chinese characters. China only switched to simplified characters after the Communists came to power in 1949, with a drive to improve literacy. At the time this scene takes place, traditional full-form characters would have been used.
At the time when he next sees his mother, Pu Yi says, "My mother has not seen me for seven years." That would make the year 1915, but it is wrong. He should say, "My mother has not seen me for four years," which makes the year 1912. In the spring of 1912, the new republican government divided the Forbidden City by constructing a wall, thus restricting the emperor's domain. Assuming that it is that dividing wall on which Pu Yi and Pu Chieh climb, one must reasonably assume that, since the wall is clearly under construction, the date is mid-1912 at the latest. If so, then Pu Yi has just turned six, not eight, and has been separated from his family for four years, not seven.
When Pu Yi walks out on the terrace during his inauguration the counting of the "kowtow" starts. At the inauguration or coronation of the emperor 3 times 3 bows should be made but you can clearly hear the count until 11.
The tour guide at the end of the film says that Pu Yi was 3 years old at his coronation. Henry Pu-yi was born Feb. 7, 1906 and invested Nov. 14, 1908, aged 2 years 10 months. However, the guide was likely using the Chinese age system, in which a person is automatically aged "1" when born.
When Johnston and Pu Yi say "farewell" to each other and as the musicians appear and follow Johnston, reflections are visible in such a way that indicate that the scene was actually shot through the glass of a pre-existing structure. The reflections are not consistent with anything else in the shot.