The movie takes place in 2259, the clock? A Lawson Model 304 "Zephyr" made around 1933, making it 326 years old in the movie. Glad to know they last! It is one of the character's alarm clock. Except the 304 has no alarm capabilities, it just tells the time. Oh movie magic!
This model was made from 1938 to 1972 with minor variations. Mine is a very early model, and still runs. The simplicity of the motor astounds me, and is probably why it lasts so long. Pennwood and Lawson used the same patented design inside their clocks, producing many clock case designs over the years. Lawson's were more upscale featuring metal cases and high polished finishes. Here is a look at what a Pennwood movement looks like.
The motor on the right, drives a gear box that constantly turns the seconds tumbler. A tab on the seconds tumbler flips the minute tumbler at each full turn. This goes on down the line until the hour tumbler gets flipped. It's a pretty cool clock to watch change time.
Now you know a little more useless information. Hope it was worth your time!