As depicted in this episode, Princess Diana and Dr. Hasnat Khan really did go on a date to see Apollo 13 (1995). Thereafter, they were in a committed relationship for three years 1995-97 and separated shortly before Diana started seeing Dodi Fayed.
Senan West plays the 13-year-old Prince William as he commences high school at prestigious Eton College. He is in fact the son of actor Dominic West, who plays his on-screen father Charles, Prince of Wales.
Prasanna Puwanarajah has portrayed Martin Bashir twice--in Diana (2013) and The Crown--different accounts of the same story.
In the scene where Diana asks "Is my heart here?" and Dr Kahn replies "I hope not." This foreshadows Diana's fatal car accident, during which her heart was displaced in her chest, which contributed to her death.