Jacquetta Woodville the mother of Elizabeth has a British accent in the show. However before she was married she was called Jacquetta of Luxembourg and would not have had a British accent.
The 15th century married women always used to wear headdresses (caps, veils, turbans) in public.
In various scenes, Henry Stafford (Michael Maloney) is seen with English Pointer dogs. This particular breed didn't exist during the 15th century. The English Pointer breed was created during the early/mid 17th century, mixing various mastiff breeds (including the "great Dane") and the Spanish "perdiguero".
Elizabeth Woodville's nails are clearly fake.