When the young Prince William's 'beak' (teacher) writes the word 'Traitor' on the blackboard during his lesson at Eton about the Gunpowder Plot, the handwriting has changes about halfway through the scene & 'traitor' is suddenly written in a much neater & clearer hand than had been used by the actor playing the 'beak' in the scene. Seems a bit of a rookie error to clean the blackboard before the whole scene was filmed.
In 1995, November 5th was a Sunday, as the script mentions at one point; but a history class is depicted at Eton on November 5th (the instructor specifically saying that the 5th is "today"). Sundays at Eton would not normally be class days.
A clip from Supersize Me/Bathroom Break (2011) is shown on television, however, this episode wouldn't premiere until 2011 while the events of this episode are occurring in 1995.
The BBC crew uses Sony U-Matic SP equipment to record the interview. This video format was already outdated in the mid 1990's.
At the start when Diana is sending Hasnat Khan away in a taxi it is clearly a 63 plate (2013). The story-line is set in 1995.