Mary of Burgundy actually died in 1482, three years before the Battle of Bosworth Field.
Prince Arthur was born in Winchester, not in London.
The palace of Margaret of York is identified as "Palace of Mechelen, Burgundy, France". However, the Mechelen area, while a Burgundian possession, was not a part of France at the time. The building shown looks like a castle in the countryside and appears to be different from the real palace, which is located inside Mechelen. Mechelen was already an important city at the time and its houses, churches, and other buildings would have been clearly visible near the palace.
Margaret of Burgundy says she lost a father and three brothers. However she actually had lost 4. She had a brother Edmund that was killed in 1460 and then her brothers Edward IV, George Duke of Clarence and Richard III.
When Elizabeth Woodville goes to visit Lizzy and Arthur after Arthur's birth she says that there is a new royal name at last. However Arthur was not a new royal name. Arthur was also the name of Elizabeth of York's half brother (the illegitimate son of her father) who she was very close to.