Sienna was never a character in the books. Anthony never felt strongly about any woman he was with. Even when he decided to get married, he didn't care about who would be his wife as long as she fit his checklist for a wife.
Daphne is distracted, and looks over the Prince's shoulder. This is considered the worst of etiquette among nobility, which includes "gazing away from them" and:
Turning your back on the royal.
Walking ahead of them.
Leaving before the royal.
Asking personal or political questions.
At the duel, the doctor asks in disbelief whether Anthony is able to guide the path of a bullet.
During that time, gun barrels were made with no rifling and the bullets were round, making them wildly inaccurate. Even at the 20 paces the men stood, it is possible for the pistols to be aimed directly on target but the bullet to still fly wide. This is also most likely why both Daphne and the horse were uninjured even though she rode directly into the firing line.
Nicola Coughlin was 31 during filming stooping to play a character supposed to be half her age.
Goof (chronological): At the ball, the performers sing Offenbach's Barcarolle, written roughly 65 years after the events of Bridgerton, which take place during George III's reign.