Throughout the series, Stephen and Matilda are both referred to as "Majesty". English kings and queens did not use the title "Majesty" until the middle of the 16th century, nearly 400 years after the setting of this series
Rectangular quadripartite rib vaults, the type of the Gothic vaults used in the cathedral's nave, appeared in the second half of the 13th century (about a century later than shown in the series).
Prior Philip is referred to by several characters as 'Father', 'a Priest' and a character at one point goes to make Confession to him.
In actual fact Philip was a monk and never a priest, so should have been referred to as 'Brother' not 'Father'. Also, in Catholic ritual only priests can hear confessions. Monks cannot.