The one way mirror between Kreer's hypnosis room and the sitting room wouldn't work. In order for a one way mirror to be effective, one side must be dimly lit (the viewing side) the other, brightly lit (the reflection side). Since both rooms were brightly lit, the mirror would be totally reflective on both sides.
As Steed leaves his apartment for the first time, Proctor punches him. Steed is knocked backwards and his suitcase bounces on the sofa and onto the floor...it was clearly empty.
Steed leaves his apartment for a taxi ride. However, the taxi sets off from the street where Tara King lives, not Steed's street.
The glasses worn by the psychiatrist when Steed visits towards the start of the episode are obviously props as they have holes drilled through the lenses for the actor to see through.
As Steed leaves his apartment for the first time, Proctor punches him. Steed is ex military and held the rank of Major and is a trained Secret Agent. He would have seen the punch coming and blocked it and retaliated in self defense.
The scenes where Proctor is following Steed and whistling a spooky tune are certainly atmospheric but nothing to do with the story. Steed's hypnotic condition means that he cannot see Proctor... whether he's whistling or not.
Boom microphone visible when Proctor and Lisa enter after Tara and Kreer's sword fight.