Thought this up last night. I'm pretty pleased; it's very goofy. Might post a rough draft up here, when/if I write it:
Imagine a world in which digital clocks really caught on; so that no one used analog clocks or watches anymore. In this world, because time appears to be quantized and discrete, peoples' perceptions of the world change fundamentally. Also, since velocity and thereby motion is based on limits and continuity, in a world with no continuous time motion becomes illusory -- you still think that you're moving, but really you're jumping from (stationary) place to (stationary) place in very small leaps. Basically, in this world, motion (and hence progress) is an illusion ala Xeno's paradox of the arrow.
This wouldn't be an issue, but it means that conceptually, this world is stalled out circa 1990. And so my hero will go back in time (using a tea kettle; you knew it was coming) and destroy (or ridicule) the digital watch in order to save continuity and progress.