Factual error: In the first scene where Dr Strange is preparing for surgery he uses improper surgical gowning technique breaking aseptic protocols. Strange puts on a mask after washing his hands, contaminating his clean hands by bringing them in proximity to the non-sterile environment of his face. Surgical masks must be worn before the full washing of hands. Another error is that he inserted his hands all the way through his gown to don gloves. Hands must never leave the sleeves and gloves must be put on with the sleeves still covering.
Continuity mistake: Strange is at home, looking for help on a video chat. His friend says no, and in his rage he sweeps almost everything off the table including the Microsoft Surface laptop. Christine enters with food, we cut back, and the area of the table to his left, which was totally clear a second ago, now has several pieces of paper on it and the laptop with a closed lid. A few moments and cuts later, the laptop is in perfect condition on the table with lid open.
Visible crew/equipment: After Doctor Strange experiments with the magical doorway in the Sanctum Sanctorum, he leaves it on a desert view and we cut to a shot panning across all the artifacts. At the very start of the shot on the right hand side of the screen is a crewmember standing in the shadows looking bored. Really blatant if you turn up the brightness, but easy enough to spot if you know what you're looking at. (00:56:00)
Other mistake: When Dr. Strange rushes a patient to brain surgery they show him and Dr. Christine Palmer operating without surgical masks. When they cut away and come back they're wearing masks. Also, Dr. Palmer is an ER doctor, and her assisting him would never happen in real life.
Continuity mistake: When Hong Kong is being destroyed, a vendor's sign falls to the ground, written in English. However, in the shot where the city is being restored, the same sign is now in Chinese.
Continuity mistake: The wound and blood on Strange's left eyebrow is first fresh, then dry, then it's gone, then is back again.