Near the end Henry VIII sits at a table upon which is a dish with many carambola fruits, also known as star fruits. The scientific name is Averrhoa carambola. He mistakenly states that these are from "the new world," thereby giving the impression they'd been brought back from the Americas. In fact, the carambola is from south-central Asia, a few islands in the Indian ocean, and southeast Asia as far as Indonesia, Malaysia, and the Philippines.
Reginald Pole was the son of Margaret Pole (neé Plantagenet) while he is a member of the Plantagenet dynasty, his mother was niece to Edward IV and Richard III. There is no evidence he attempted to lay claim to the English crown. He was named Papal legate to England and charged with encouraging the Pilgrimage of Grace. His story may have been confused with Richard de la Pole who was the last member of the Yorks ( a cadet branch of the Plantagenet) to try and lay claim to the crown.
Patrick Gibson who plays Askes son would later go on to play "The Boy" or Perkin Warbeck who claimed to be Prince Richard Duke of York the son of Edward IV and Elizabeth Woodville in the Starz TV show The White Princess with some scenes bring used in their follow up series The Spanish Princess.