Wardrobe continuity error. When Diana first encounters Matthew in the library, when we see his hand catching the book which flew off the shelf, he is wearing a charcoal wool blazer. For the remainder of the scene he is wearing a regular black suit jacket or blazer instead. The charcoal wool blazer does make an appearance again for a subsequent scene.
Diana requests and receives several volumes at library but is only seen to return one.
White cotton gloves are absolutely required when handling ancient or rare books, especially at Oxford, with any from the Ashmolean gift.
Just before James is hit by the car you can see him brace for the impact.
Diana calls Sarah who is in upstate New York, complaining that it's 5:00 am. But there is bright sunshine outside. While there might be sunshine at 5:00 am near the Summer Solstice, the opening captions had established it's the Autumnal Equinox.
At the beginning of the episode, Diana is shown drinking from a mug as she hurriedly eats her breakfast. The price sticker and barcode can be seen still stuck to the bottom of the mug.