The way they demonstrate that David (Keir Dullea) is disturbed is by having him be really twitchy about knowing the exact time. There's a scene where he raves on and on about how wonderful it would be if everyone had a watch that could synchronize itself somehow to a central clock, and everyone would know the correct time....
My response is "and this is a problem why...?"
This is especially ironic these days, since almost everyone's cell phone synchronizes its own clock with the cell network -- and cell phones (amongst other things) are driving a decline in watch sales.
Moral: one generation's neurosis is another generation's basic expectation.