"Therefore, for goodness' sake, and as you are known..."
See in text (Prologue)
"For goodness' sake" has its literal force and meaning here: "for all that is good and decent." The prologue to Henry VIII asks the play's audience to be serious for goodness' sake—that is, politeness or kindness.
"For goodness' sake, consider what you do..."
See in text (Act III - Act III, Scene 1)
Cardinal Wolsey—an ambitious and potentially treacherous a man—urges the queen to change her childish and sulky behavior. He uses this expression to invoke goodness in a more abstract way, akin to saying something like "be good for the sake of being good." While this may not appear meaningful, its applied force is more in its use as an exclamation to call attention to her actions.
"Farewell! a long farewell, to all my greatness!..."
See in text (Act III - Act III, Scene 2)
Cardinal Wolsey has strong ambitions, but his plots were eventually exposed. He calls after his antagonists in this passage and then starts this meditative soliloquy. By "greatness" he means "power," and his farewell to this power is ironic because he is still the cardinal. However, he currently sees his fortune reversed as if a "killing frost"—an evil force—were working against him. Notice how in his despair he actually compares himself to Lucifer, the archetype of ambition.
"She had all the royal makings of a queen..."
See in text (Act IV - Act IV, Scene 1)
The point of interest in this expression is "the makings of." This is the first recorded use of the phrase, which means something like "the potential to be" or "the things one is made of." The Third Gentleman is using it here to describe the coronation of Henry VIII's second wife. Shakespeare uses the expression similar to how we understand it, but in this context it has a little more meaning, something like "the trappings of or "the symbolic distinctions of."