OK, I was rethinking what I said in my last post about leap seconds. What I said is kinda technically correct, but I should be clearer.
I said that the tides from the Sun and Moon slow the Earth, and that's why we need to add leap seconds every now and again. But even if we were to remove that effect, we'd still need to add leap seconds. Why?
Imagine you have two clocks. One thinks there are 86,400 seconds in a day, the other thinks that there are 86,401, so the second clock runs a tad bit slower than the first. Every day, it's one second behind, clicking over to midnight one second after the first clock does. Mind you, it keeps accurate time according to its own gears: every day has 86,401 seconds, so it's not slowing down.
However, to keep it synchronized with the other clock, we'd either have to subtract a second from the second clock (yikes, terminology is a bit confusing there!) or add one to the first clock every day. So we'd need a leap second every day, but not because the clock is slowing. It's only because it runs at a different (but constant) rate.
Same thing with the atomic clock and the Earth. The folks in charge of measuring time needed a standard day length, and so they chose the length of the day as it was in the year 1900. But the Earth has slowed since then, and continues to slow. However, even if we could remove the influence of the Sun and the Moon, the Earth would still be rotating at a different rate now than it was 109 years ago. That rate would now be constant, but slow compared to the standard day. So we'd still have to add a leap second to the atomic clock to match the slower Earth. In fact, one is added almost every year now.
This is a subtle but important effect. It's easy to simply extrapolate how much the Earth is slowing and say, hey, it'll stop completely in a few thousand years (I've seen creationists make that claim). But that's not correct; we're only talking about adjusting for two different rates, which gives an accumulated difference. That would happen whether the Earth continued to slow or not.
The Naval Observatory page has more about this. I hope I didn't confuse anyone in that previous post.