As Blackadder is going through the list of possible wives for George he mentions Caroline of Brunswick as the only available princess but dismisses her as having a horrible personality. In real life, George did in fact marry Caroline of Brunswick (his first cousin) but the marriage happened before George assumed the regency, and after George was already illegally married. George was reportedly drunk during the ceremony and wedding night, and the marriage was an unmitigated disaster: Caroline lived most of the marriage in exile, with George trying (unsuccessfully) to divorce her; after his ascension as king, he attempted to prevent her from becoming queen (he was unable to keep her from being named queen, but had her barred from attending her own coronation); and his supporters twice put her on trial for adultery using trumped-up evidence. Their only child, Princess Charlotte, died giving birth to a stillborn son; with no legitimate heir, George was succeeded by his brother William.
The Shadow voice over is not credited.
When Blackadder is searching for somebody to marry the prince, he comes up with one princess, Caroline of Brunswick. The real prince regent (later George IV) did marry a Princess Caroline of Brunswick, but as a testament to George's eternal stupidity he did not attend the wedding himself he sent his best friend Buckingham as a stand in.
The scene in which Blackadder is telling George what to say to Amy as he stands beneath her window, and later pretends to be George himself to woo her, is a direct reference to the famous scene in Edmond Rostand's 'Cyrano de Bergerac.' Coincidentally, Blackadder's first name is also Edmond.