When I was a kid in school I noticed that all the analog wall clocks in the school would never drift from each other. They might have had differences in their displayed time but the differences were constant to the second even through a whole year, while watches and battery-powered desk clocks would drift. Always wondered if they were sharing a timing source.
Such clocks indeed use a central timer. Same as station clocks, the minute hand runs slightly fast and is mechanicly halted at the 12 by a central controlled magnetic clutch.
2 fun facts about the 60 (50) Hz AC power: It varies primarily due to load on the grid. It will fall < 60 when demand is growing and exceed > 60 when the demand is falling. Also, this variation can be logged and used to time stamp many audio/video for forensic purposes. Also, many simple clocks do not work in remote locations that have diesel generators because the 60hz is not stable.
An early electric clock based on mains frequency was developed by Nikola Tesla. It is also interesting that before the standardization at 50 and 60 Hz there were tens of frequencies in use like 40, 42, 133 and 25 Hz.
Old record players and tape recorders also use synchronous AC motors to maintain the correct speed. They have pulleys of different sizes depending on the frequency of the countries they are designed for. In Japan, the frequency you get depends on where you live as both 50 & 60 Hz are used there.
All the generating stations on the grid do maintain a common frequency, but the frequency does vary slightly from 60 Hz (in the U.S.) in response to changes in the power demand and power supplied. Over the long term, the frequency is made to average exactly 60 Hz so there is no accumulated error in the clocks that depend on the frequency.
Replaced heaps of analogue timers, the plastic gears always break down over time. In Australia we have these Zellweger relays that put 1050Hz down the power lines, operating 1000hz above our typical 50Hz doesn't effect such analogue timer designs.
The majority of countries in the world (~80%) are 50 Hz, not 60 Hz. Imagine that - there countries other than America. en.wikipedia.org/wiki/Mains_electricity_by_country