Catherine Howard may have been as young as 15 when Henry first met her.
The execution of Thomas Cromwell is considered apocryphal, some accounts depict the executioner having difficulty severing Cromwell's head. However, others say he had no trouble at all. The depiction in the episode is similar to how Margaret Pole (Lady Salisbury) is said to have been executed; her execution had issues severing her head, hacking at her shoulders and head.
There is a bit of a question with the annulment between Henry and Anne of Cleves. When looking into her pre-contract with the Duke of Lorainne's son they determine that she had in fact been essentially married to him. However when Edward Seymour tells her of the annulment he tells her that she is free to remarry. Both things can not be true, if she is already married to someone else she should not be able to get married again to someone in England.
Sarah Bolger (Mary Tudor) and Colin O'Donoghue (Duke Philip of Bavaria) later work together in the TV show, Once Upon a Time (2011), playing Princess Aurora and Captain Killian 'Hook' Jones respectively. Curiously, Aurora's love interest is also called Phillip (Prince Phillip, played by actor, Julian Morris).
Thomas Cromwell talks go his son Gregory about Gregory's wife and baby. They don't mention that Gregory's wife was the sister of Jane, Edward and Thomas Seymour making Gregory their and the Kings brother in law.