Queen Charlotte gets mad that her daughters have not had any babies. In real life several of her daughters wanted to get married early in their lives but Charlotte and George denied them. Several daughters did get married but all were married in their early to mid 40s when there was little chance of having children.
The queen is told that the Princess Royal has died. The queen's daughter Charlotte did not die until 1828, 10 years after the queen. It was the queen's granddaughter, also named Charlotte, who died in childbirth in 1817. At the time, only five of her thirteen living children were married and had no legitimate children among them. (Her third son, the future William IV, had 9 living illegitimate children at the time.) Four of her children would marry in 1818 and Victoria, who would eventually inherit the throne, was born in 1819.
Queen Charlotte's children are seen to be in the mid 20s-early 50s. In real life by the time that is portrayed her children were in their late 30s-mid 50s.
Many men in the 1760s are seen not wearing wigs when they should be, either as members of the nobility or household staff, particularly: King George III, Reynolds and Brimsley. In the 1760s, the fashionable wig shape had a flat top and styled brushed out curls on either side, with the rest of the hair pulled back into a queue. Most wealthy men didn't start wearing their natural hair until the 1780s, and even then they generally powdered it to look white and kept it long; natural and short haircuts only became popular in the 1800s.