I've got 2:

-Your clock works the way you think it does

I was working for a company that makes pico-second clocks. It turns out, that all clocks experience drift. Like a gyroscope, each clock has it's own peculiarities and hyper-local environment, and like a gyroscope, they all tend to record and count time in different ways. If you have a clock, you know what time it is. But if you have 2 clocks, you are never sure. Now, we extend this to many clocks and we then have an ensemble of them, and (thank god) it ends up being a normal distribution that we then take the mean of. Now with picosecond clocks, the local gravitational environment, temperature, wear history, etc all end up being very big factors in time keeping. For most systems, this would be a catastrophe. You'd have to bury the clocks in some mountain, gravitationally 'shielded' away from things, temperature controlled, super clean, etc, and only take the time once a day or something. It turns out that if you run those calculations, you can only keep time to a part in 10^-16. Fortunately though, we discipline time to that of the Earth. Days and years are the thing we must subside to. And these things are only good to about a part in 10^-12, so we have 10,000 parts of 'error' to live in. It turns out, the Earth is a pretty bad clock, overall. It was pretty cool, years after I left that job, to walk into NIST and see an ensemble of our old clocks in the room where the US second is measured.

-Leap seconds always occur on the same date/time of the year.

The terrible earth-quake in Fukushima really did a number on the international timing community too. The change in distribution of mass of the Earth was so much that it slowed the year down by ~1 millisecond in total. I hope that the readers of the article and the rest of the comments here can appreciate that such a change, though to a normal person is small, is actually quite a lot for computers and other logic based systems. The 'leap-second', in reality a millisecond, was chosen to occur not on the last night of February of the following year, but was pushed forward to the last night of June. This did not make the people that sell super precise clocks very happy. Typically, the leap-second night is one of mayhem for clock sellers and the people that support the sold clocks. As this usually happens at midnight, far past when you have to put your kids to bed, the 'push notification' of the new time is in weary hours. That means starting about 1 minute after midnight, you start getting flooded with calls from your customers. Now, the purchasers of hyper-precise clocks tend to be very wealthy and powerful and very angry and sleepy that all of their very expensive computers are now 'all broke'd' in the literal middle of the night. Most of the time, you can reach out to the IT guys of these large oil&gas, Wall-Street, military, educational, and other types of firms and make contacts and let them know things will start to get out of whack. And they tend to learn that this usually happens in early March. Well, for this end of June leap-second, we knew things were going to be hairy. And they were. I was not even close to senior enough to be on those calls, but I came in the next day and all the senior guys were STILL on the phones with the various companies. When I left, they were on the phones still. I think they must have been up for at least 50 hours, judging by the amounts of RipIts scattered about the floors. That is what I call a salary job.

In all, I learned that humans think that time works in one way, but it really is 'what a clock measures' and is an abstract concept we put a lot of value into. And no, we will never be able to make a program that can take all of these considerations into account. All that will do is make the troubleshooting process a lot longer. Time is ephemeral, the Earth makes a bad clock, and mammals are diurnal. Those 3 things make clocks and time-keeping a 'hands on' job.