It was Mary, Henry's younger sister, not Margaret, who was in love (and later became his wife) to Charles Brandon and was sent abroad to marry a feeble old king. This king was Louis XII, king of France, not king of Portugal. He died 10 years before king Francis was captured in Pavia by Charles V armies (not at the same time, as we are shown).
In 1525 (the year that Charles V armies capture Francis in Pavia, which occurs at the same time in the episode) Portugal didn't have a sick old king. John III was only 23 years old and he married Catherine, Charles V sister, precisely in 1525.
Henry VIII sends his sister Margaret to marry the King of Portugal. In fact, Margaret Tudor was married to James IV of Scotland. Later she married the Earl of Angus and after that Lord Methwen, Henry Stewart.
When Brandon is talking to Margaret in her room on the ship to Portugal we can see the hanging lamps swinging, and the camera swings too, but the wine in the one glass on the table does not move and the glasses themselves stand still.
During the wedding of Margaret Tudor with the king of Portugal, the hymn sung is the "Ave Maria", by Giovanni Pierluigi da Palestrina, born about the supposed time of the (fictional) wedding (ca. 1525).
Margurite de Navarre comes to Court. However she was only Margurite de Navarre after she was married to her second husband which did not take place until a year after the events of the episode.
The landscape of Lisbon on this episode features the University of Coimbra (some 150km north of Lisbon) clearly on the top left of the screen.
Even though you hear clear Portuguese by the steward, King Manuel's speech is actually mangled Spanish. Also in the scene, some of the background speech is gibberish.