Revealing mistake: As Veruca sings "I want it now" in the egg room, the plastic seams on a few of the golden eggs are quite visible, along with their 'dimpling' near the tops and bottoms, as the Oompa Loopmas pass them around for polishing.
Visible crew/equipment: When everybody first comes in the main room with the chocolate river, there is a shot of all of them standing in the doorway. At the bottom of the scene is the shadow of the camera.
Visible crew/equipment: In the Fizzy Lifting Drink scene, as Wonka leaves the room, a bubble machine is just visible at the bottom left of the screen.
Other mistake: During the glass elevator ride, first Joe points out their house can be seen but then when the area is shown on camera, no little house like theirs is in the shot. Next, Charlie says he sees his school, and again when the shot looks down below, no school at all is seen, but rather just streets that come together through a small tunnel and random houses.
Answer: Closed circuit security was invented in 1942 and came into common use in the late 60s and early 70s. Beyond that, Wonka could have had Oompa Loompas monitoring the group or simply noticed that they were gone and guessed.
Greg Dwyer