After searching the house of Lady Dibdale, Robert Catesby (Kit Harington) grabbed Sir William Wade, at which time Wade's guard put his sword to Robert Catesby's neck. The next camera angle clearly shows his neck with no sword near it. It's not until the following shot that we see the sword being moved from his neck down to his chest.
King James is shown using the bathroom in front of his dressers/courtiers. The Monarch ALWAYS did his "business" in private, accompanied only by The Groom of the King's Close Stool, whose job it was to assist the Monarch in the performance of his "business", and personal hygiene. During the reign of James's predecessor, Queen Elizabeth I, The Groom of the King's Close Stool was replaced by the First Lady of the Bedchamber; James revived the office as The Senior Lord of the Bedchamber.
Catesby insinuates to Father Garnet that his wife died in childbirth. Robert Catesby was born in 1595; his mother, Catesby's wife, died in 1598.
When the conspirators look out of the window towards Westminster, the Abbey is shown with its two towers by Nicholas Hawksmoor, not built until 1722-1745.
Dozens of bright red candles adorn the set. Colored candles were not in existence prior to the 20th century. In the 1600s they would have been the color of rendered fat. Candles were made from tallow.