Continuity mistake: In the post office scene, when Cindy is talking to her dad, you can see a post box marked "Grinch" and it has nothing in it. Later we are shown a close-up of the Grinch mailbox and it has spider webs in it.
Visible crew/equipment: After the Grinch takes the little car, in one of the shots you can see a stage light behind him. (00:57:25)
Visible crew/equipment: When the Grinch is building the sled as he is putting the tin sheets on it there is an overview shot where you can see the shadow of the camera. (01:01:01)
Answer: By machine.
The clock in "How the Grinch Stole Christmas" is designed for cinematic effect; a real-world counterpart would rely on precise gearing and engineering to allow three separate wheels to operate in close proximity without interfering with each other. The key would be in the gear ratios and the alignment of the gears to ensure smooth operation of each panel.