First of all, there are a few aspects to deal with: the heights that people have recorded have changed simply due the change in the precision of our instruments, but now that our measurements are quite precise, we also know that the height of the mountain actually does change a bit every year.
In terms of measurement error, here is a good example: "The observations made in 1954 varied by 17 feet; the margin of error in the 1999 calculation was only a fraction of that."
In terms of the actual height, It seems that there are two competing forces. On the one hand, the collision of two continental plates (Asia and India) causes a certain amount of uplift each year (perhaps about a centimeter or so per year, although there seems to be some disagreement). On the other hand, other forces, such as erosion and melting glaciers can cause a decrease in height (see here and here). So, it's unclear how much it changes each year, although the height is never exactly constant.
Ultimately though, it's a matter of scale. If the height of Mt. Everest is the same, rounded to the nearest foot (or whatever your unit of choice is), for hundreds of years, some would say we can count this a long-term fact. While it's probably not true for Mt. Everest, perhaps it's more accurate to say that the fact that Mt. Everest is the tallest mountain is a long-term fact (though we have only known this for a hundred and fifty years or so), while it's height is a mesofact. Apparently though, Mt. Everest is moving laterally at quite a nice clip: 6 centimeters per year, so it's location is also a mesofact.
(thanks to everyone for feedback on this)