Continuity mistake: In the wide shot of the town square after the mayor says there "is no Grinch problem here!", the yellow car that had a full cab that the red car hit is missing, and the red car's right headlight that was knocked out in the crash with the yellow car is back in place.
Continuity mistake: After Cindy thanks the Grinch for saving her, he stops at the door. He slides his hand down the glass, and it comes off the glass well below his chin level. When he turns around, it's just at his chin height.
Continuity mistake: When Lou enters the classroom, the teacher's yardstick switches position from straight up and down to flat as the shot perspectives change.
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.