During the scene where Georgiana introduces her daughters to Bess a couple walking a black and white dog walk past. They are then seen further along the river before disappearing from the shot. They then pass in front of the camera again at the end of the scene.
When Mr. Grey and the Duchess meet by the lake (where they give their first kiss), the Duchess' hairdo is complimented with a rose above her right ear, which, according to the camera angle, is covered/not covered by her hood.
Georgiana, Duchess of Devonshire was born in 1757. Charles Grey was seven years younger, born in 1764. According to the subtitle, the scene depicting a wager among the young ladies over a footrace between Charles Grey and other young men was held in 1774. Georgiana was correctly seventeen at the time, but Charles Grey was ten. He would have been a boy, not the young man about to attend Cambridge portrayed in the film.
The scene in which Georgiana goes into labor to deliver her first baby, begins at night on a snowy evening. This would have been her first baby girl that was later named little G, for Georgiana. However, the real Little G, was born on July 29th, far from what would have been a snowy evening.
In the last scene with the kids running around the fountain. Fountains have been created for hundreds of years running on gravity, not electricity. For example, the Trevi fountain in Rome was completed in 1762, and the Emperor Fountain at Chatsworth was completed by Joseph Paxton in 1844.
In the scene with the little girls in the carriage, when they print on the screen the names of Harryo, Little G, and Charlotte, they mix up Harryo and Little G's names. Harryo is the youngest, with the dark hair, but they put the name "Little G" in the front of this child and put "Harryo" in front of the blond older child. In a subsequent scene, Harryo, the youngest with the dark hair, falls and scrapes her knee. Georgiana specifically calls her by name, Harryo. In fact, Little G was older than Harryo. So the scene with the names is incorrect, while the scene with the scraped knee is correct.