Factual error: Whilst hanging, drawing and quartering was indeed still the prescribed penalty for treason (and would remain so for the most serious offences until 1870, although the Newport Chartists were the last to actually receive the sentence), this barbaric punishment had not actually been carried out since the 17th century. By the 19th century the condemned person was hanged until dead and the head then symbolically severed by a surgeon. Nobody, least of all Lord Melbourne, would have believed in 1839 that the full punishment was going to be carried out, but they all talk as though they expect it to be.
Factual error: When Victoria and Albert visited Blair Atholl in 1844 (actually two years before the events depicted in the previous episode, which occurred in 1846), the Duke of Atholl was mad and locked away in a London townhouse, as he had been for 46 years. The man who hosted them and is depicted by the 70-year-old Denis Lawson was actually his nephew and heir, Lord Glenlyon, who was then only 30 and succeeded his uncle as duke in 1846.
Factual error: Drummond's assassin is said to have been a farmer who was angry about the repeal of the Corn laws. He was actually Daniel M'Naghten, a woodturner who was found not guilt by reason of insanity and was under the delusion he was being persecuted by the Tory Party. Drummond did not take a bullet for Peel. Peel was not with him at the time. M'Naghten mistook him for Peel as he left Peel's house and shot him in the back.