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?"
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.