Shakespeare mentions clocks 37 times in his complete works. A clock is a useful way of marking the passage of time to create the illusion that events on the stage are occurring in real time and so build up the dramatic tension . In Julius Caesar (Act II, Scene 1) Cassius announces that "the clock has struck thrice" In Measure for Measure the Provost announces that Claudio will be executed at four of the clock. (Act IV, Scene 2). In As You Like It Orlando comments that "there is no clock in the forest" (Act III, Scene 2) indicating that in a rustic setting life moves at its own pace. In Merchant of Venice Gratiano says "lovers ever run before the clock" (Act II, Scene 6) illustrating the urgency of desire. In Loves Labour's Lost (Act III, Scene 1) a Biron seeks "a wife that is like a German clock". Verpsrung durch Technik perhaps! And in Twelfth Night Olivia comments that the clock is upbraiding her for wasting time (Act III, Scene I).
But how good were the clocks in Shakespeare's time? The truth is not very accurate. The Romans used water clocks (Clepsydra) which in their simplest form comprised of a water filled upper container with a small hole from which water flowed slowly into a second lower container which could be calibrated during the day with a sundial. The upper container could then be filled in the evening and used to tell the time during the night. In some towns and cities an attendant would strike a bell to sound out the hour. In the mid 14th century many simple clocks were made from wood but in truth these were little better than the water clocks used by the Romans. Here is an example from the British Museum dating from around 1377. Clocks were powered by falling weights and a loss or gain of one hour in a day was considered acceptable.
By Shakespeare's time metal had replaced wood for clock construction but clock accuracy was still not good because the pendulum had not yet been invented. Galileo did propose using a pendulum to improve clock accuracy but he took this no further than concept. Inaccurate timekeeping was a problem for astronomers like Tycho Brahe who introduced an uncertainty factor to his measurements of the night sky to account for inaccurate timekeeping. In Shakespeare's time many clocks were decorative items designed to show off an owner's wealth or status but inaccurate for scientific study or precise measurement.
This example from the British Museum dates from 1560 but only has one hand to mark both the hours and the minutes. Many clocks had a revolving dial with the constellations shown. If the clock ran down it could be restarted and the constellation ring used to the align the clock dial with the night sky to get the right time like a ship's nocturnal.
However, Shakespeare obviously knew about clocks and had seen many of them and so must his audiences to have understood the many references to them and the passage of time in his plays.