After the real Hilda Stern kills the prison guard, the woman who enters the cell and pulls the cover off the body touches her face to see if she's dead. The guard blinks.
When Moss answers the telephone, it continues to ring after he has picked up the handset.
Felder introduces the real Hilda Stern to Manning. As she enters the office, she holds the door fully open, and then releases it behind her as she approaches Manning. The door swings very slowly! When the door is about two-thirds closed, a movie camera wheels into view (pointed in the other direction), and then the back of a cameraman.
In the closing moments of the climactic scene where Steed and Mrs. Gale capture the lead criminals, Catherine reaches for the telephone to call the police. A cough can be heard in the background from one of the crew, there being no scripting for a cough required from one of the actors.