I always get this episode confused with “The Danger Makers” for some reason. This is the one where geniuses are being hypnotized into devising impossible crimes. It’s another extremely well paced mystery, and while grownups are probably going to figure it out without much strain, it’s certain to tax the brains of six year-olds. Fortunately there’s enough going on to keep the story fascinating for him, and he followed along, with a little help, quite well!
Of note, there’s one of the rare scenes in the series where Steed gets incredibly angry with someone. A character played by future Monty Python’s Flying Circus producer Ian McNaughton kills someone while under post-hypnotic suggestion and it looks like Steed’s going to make sure he’s next. Other parts in this story by Robert Banks Stewart are played by Bernard Archard and Patricia Haines, who we’ll see in a very memorable role in the first color series down the line.
Fire Breathing Dimetrodon Time 
There’s a remarkably cute bit of set dressing in this episode. Most of the action is set in a girls’ boarding school during the winter holidays. (I assume it’s winter as it seems the sun goes down between six and seven.) Steed’s room has a wardrobe or closet with pin-up photos of shirtless men taped all over the inside, and the room’s usual owner has left her stuffed gollywog behind while going home for break. It genuinely feels like a real place with a real occupant.