Catherine asks Henry to delay her confinement until all souls day which is November 1 so she can pray for a son and heir. Shortly afterward Mary is shown being born even though she was born in February.
Princess Mary is shown being born at almost the same time as the wedding of Henry Stafford and Ursula Pole. While both events happened in mid February Mary was born in 1516 and Henry Stafford and Ursula Pole were married in 1518 or 1519 two or three years later.
The 'Groom of the Stool' was the first gentleman of the King's privy chamber, a highly intimate and sought after role. Margaret Pole would not have been disgusted by or condescending toward William Compton for holding this position.
Margaret Tudor is shown secretly married to Archibald Douglas, Earl Angus when Catherine is heavily pregnant with Mary. Margaret and Archibald married in 1514 and Mary was born in 1516 so there was a 2 year gap between the two.