Revealing mistake: After the Grinch burns down the Christmas tree in the middle of town and right before they bring out the new one, the Grinch is about to make his escape in the Dump it to Crumpit. The Grinch makes a wide eyed face and you can see he isn't wearing his green and yellow contacts. (00:59:15)
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.
Continuity mistake: After the Grinch answers the cop's greeting with "Flatfoot!", two Whos carrying packages pass by him, and he watches them pass. As the Grinch approaches two Who children to give them the hacksaw, the same package-laden Whos pass by again.
Continuity mistake: The Grinch holds the electric razor in his palm, then grasps it finger by finger. The next instant cut shot of him shows him holding the razor, but his hand is open.
Other mistake: When Lou and Cindy-Lou come home, Betty asks Cindy-Lou to unscrew the bulb in the refrigerator. A few moments later, Lou answers the phone, and repeats the question "Is my Sub-Zero Chillabrator running." Betty seems to have used an un-Who like term.
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.