After his character collects Columbo from Heathrow Airport, John Fraser, who has spent nearly all his career in the UK, only appears in scenes filmed outdoors, as part of the restricted filming in Britain.
When Columbo walks down the small spiral staircase to the waxworks museum's storage basement, the staircase with the octagonal light above it is the same set as used in the previous episode "Etude in black" for the club where the trumpeter (James Olson) is playing.
Only certain location shots, and one interior scene (Columbo's visit to Superintendant Durk's gentleman's club) were actually filmed in Britain. The rest of the studio scenes, and all those taking place at Sir Roger's country house, were made back in California.
The title comes from the famous soliloquy in William Shakespeare's "Macbeth" (Act II, Scene I, lines 33-39): "Is this a dagger which I see before me, / The handle toward my hand? Come, let me clutch thee: / I have thee not, and yet I see thee still! / Art thou not, fatal vision, sensible / To feeling as to sight? Or art thou but / A dagger of the mind, a false creation, / Proceeding from the heat-oppressed brain?"
Inside joke: "Lillian Stanhope" (Honor Blackman) says "I've always wanted to be in a horror movie." 'Dagger of the Mind' aired on 11-26-72. Just six months earlier (5-30-72), the horror movie 'Fright" was released, which featured Honor Blackman.
The trivia item below may give away important plot points.
A very important scene at the end of the episode was deleted from the original print, it is not shown in reruns. It comes after Basehart and Blackman have been taken away. Columbo shows the inspector how he knew there was a pearl in the open umbrella display by "thumb shooting" a pearl into a cup being held by a wax figure. He had shot one in the umbrella when he turned to cough. As he is demonstrating, Columbo says "How do you get a girl's attention in class at school?".