Rachel McAdams' startled reaction in the broom closet was genuine, since the mop handle fell completely by accident, and scared McAdams almost out of her skin. Scott Derrickson decided to keep the reaction in the film, since she never broke character.
Mads Mikkelsen admitted that with all the computer-generated imagery he got a bit lost on how to film his scenes, especially during the Mirror Dimension scenes.
The Eye of Agamoto is the Time Stone, one of the Infinity Stones. Chronologically it is the fifth Infinity Stone to appear, after the Space Stone (the Tesseract from Captain America: The First Avenger (2011)), the Reality Stone (the Aether from Thor: The Dark World (2013)), the Power Stone (the Orb from Guardians of the Galaxy (2014)) and the Mind Stone (Loki's scepter/Vision's power source from The Avengers (2012) and Avengers: Age of Ultron (2015)).
(at around 1h 28 mins) The scene where the Cloak of Levitation wipes away Strange's tears was improvised on set. It was a suggestion Benedict Cumberbatch made to the crew, who liked it enough to create it.
Chiwetel Ejiofor is a fifth-degree black belt in karate, so his movements are second nature in fighting.
Stan Lee: (at around 1h 18 mins) man on the bus reading "The Doors Of Perception" by Aldous Huxley. The book is a recounting of Huxley's experience taking psychedelic drugs, with particular mention of their use in perceiving art. Dr Strange comics have long been associated with psychedelic drugs because of their use of surreal images to portray magical dimensions and beings. Marvel has always insisted that drugs played no part in the creation of Dr Strange, which may be why Lee is laughing at the book.