In the excommunication scene, which took place in 1164, the monks are chanting the Dies Irae, a hymn said to have been composed by Thomas of Celano, who lived from 1200-1260. The hymn is also heard in the opening scene as Henry walks through the cathedral, which would have been in 1173.
Although the story takes place in the late 12th century, the armored helmets that King Henry's children play in are right out of the 15th century, the same as one might see in films about Joan of Arc, or Henry the IVth and Vth. This choice by the costumers must have been purely aesthetic because the armor of the last 100 years of medieval times was by far the most splendid visually.
Contrary to one of the film's central plot lines, Thomas à Becket was a Norman (Thomas Bequet), not a Saxon. Jean Anouilh admitted he discovered this after having finished his play, having based it on the outdated 1825 work "The History of the Conquest of England by the Normans", by Augustin Thierry; but he decided that it made a better story the way he had written it.
When Henry II's men come to Canterbury to assassinate Becket, Becket is facing the altar. The long shot shows Becket walking toward them in the distance. The next shot shows Becket still facing the altar.
During the assassination scene, Brother John raises the silver cross to strike a soldier. When the camera angle changes after John is stabbed, he has no cross, though it isn't shown or heard being dropped.