On the DVD director's commentary, Kevin Macdonald states that during filming of Idi Amin's visit to the village near the mission, many of the local extras thought it was the real Idi Amin on stage giving speeches.
Idi Amin's full title was as follows: "His Excellency President for Life, Field Marshal Al Hadji Doctor Idi Amin, VC, DSO, MC, Lord of All the Beasts of the Earth and Fishes of the Sea, and Conqueror of the British Empire in Africa in General and Uganda in Particular."
In an early scene, Idi Amin playfully trades sparring punches with a group of Ugandan boys. It isn't mentioned in the film, but Amin was a champion boxer. He was Uganda's light heavyweight champion from 1951 to 1960.
Amin had several British doctors in real life, but not a Scottish one. The character Dr. Nicholas Garrigan is loosely based on Bob Astles, a British soldier and diplomat who was one of Amin's confidants, but who fell out of favour with him, and was temporarily sent to Makindye Prison, one of Uganda's most brutal prisons.