It's only one second, while quite interesting I don't see why this matters
The only people that a leap second realistically affects are astronomers and they are more than capable of managing their own time software.
At roughly 1 second every 1.5 - 2 years it will be a couple of millenia before the sun even gets an hour away from local noon - and people manage with daylight savings time. So every 2000years we might need to introduce a leap hour.
First, you have to be precisely in the middle of a timezone, and not one of those weird timezones that doesn't actually follow the lines of longitude, either. Otherwise you're skewed late or early relative to solar time. Secondly, solar noon even at the precise center of timezones is only local 12:00 on average, because the timing of solar noon vis-a-vis a 24-hour clock fluctuates through the year by up to 18 minutes. Two factors are involved: the Earth's orbit is slightly eccentric, and Earth's axis of rotation isn't precisely perpendicular to the plane of its orbit (http://en.wikipedia.org/wiki/Equation_of_time has details and a graph).
So all the leap seconds do is keep the average local noon, at precise centers of timezones, equal to solar noon.
But when the clock jumps back abruptly by 1.0 s, the controller gets confused. Its next control loop update cycle is now scheduled 1100 ms into the future instead of the normal 100 ms period. This delays the motor shutdown signal and even causes the controller to miss the top-of-position sensor. The elevator car slams into the roof of the building. The cable snaps and all passengers contemplate Einstein for 10 s as the elevator car freefalls to their certain doom.
Well they would have, except that cable elevators have had mechanical safeties for a backup system since the 19th century.
OK, so instead:
Picture yourself receiving life-saving radiation therapy, when the clock strikes midnight ...