At the dinner party at the beginning, a portrait of Captain Blackadder from Blackadder Goes Forth is positioned on the wall behind the present Blackadder.
Although not correct to the period, black extras can be seen in the Robin Hood and Elizabethan scenes. This is because of a long-running joke between comedians Richard Curtis and Lenny Henry who apparently always complains that he could have been the extra instead.
Regarding Blackadder's cunning plan to become king, Baldrick asks if it is as 'cunning as a fox what used to be Professor of Cunning at Oxford University, but has moved on and is now working for the UN at the high commission of International Cunning planning?'. This is building on a line delivered by a previous Blackadder to his Baldrick in Blackadder Goes Forth: Goodbyeee, involving a plan 'as cunning as fox who's just been appointed Professor of Cunning at Oxford University'
In the opening credits, there is a photo of Blackadder in Indian attire. This is a homage to Rowan Atkinson's wife Sunetra Sastry, who was makeup on Black-Adder II and is of Indian descent.
The trivia item below may give away important plot points.
This is the second Blackadder to have made it as King of England. His ancestor from The Black Adder made it as King in the finale (though for less than a minute), while his Black-Adder II and Blackadder Goes Forth ended up dead and his Black Adder the Third lived out his life as a Regent.