Mr. Brock refers reporters to a pair of employees named Shuster and Siegel. Jerry Siegel (writer) and Joe Shuster (artist) are the creators of Superman.
"Doctor Misterio" (without the "y") is the name given to the Doctor Who (2005) series in Mexico. Steven Moffat and Peter Capaldi went to Mexico as part of the Doctor Who World Tour and Capaldi became mildly obsessed with the name. Because of this it became one of the inspirations for this episode.
Just after the 39 minute mark, a theater marquee is shown. The marquee says "Mind of Evil now showing." "The Mind of Evil" is a third Doctor adventure featuring the Master.
The large time distortion fixing machine/device the Doctor is making on the roof of young Grant's building is to fix the local time distortions, which the Doctor admits to being the cause of-referring to "Angels in Manhattan", in which due to the paradox created by Amy and Rory, the TARDIS couldn't return to go back to New York again.
Charity Wakefield's character is named Lucy Lombard, a clear reference to how several love interests of Superman had alliterative names beginning with L, including his eventual wife, Lois Lane.