Many of the hand-waved Union Flags during the Royal visit are upside down on their sticks.
Morse mentions that he has been back in Oxford for "a couple of months", which would indicate a time period of no later than late summer; however, when he and Alice speak out of doors, their breath is misty, suggesting it is the depth of winter.
Near the beginning, DS Peter Jakes says to Morse, "Didn't get your invite, then?" The word "invite" is a verb, and while it may be used as a noun today, in the 60's the noun "invitation" would have been used.
When the Crown Prince arrives at the Broom's estate in his huge limousine, he is actually riding in the cramped folding jump seat. It makes the scene of him exiting the car a bit more dignified, but it is hard to believe anyone of his status with a car like that would travel about in the most uncomfortable seat available.