Warning: this is yet another of my "book length" answers... :-)
Let's start by a quick review of how a zoom lens works. Consider the simplest possible lens design -- a single element. One big problem with a single element lens is that the focal length of the lens determines the distance the element has to be from the film plane/sensor to bring a scene into focus, so a 300 mm lens (for example) would have to be 300mm away from the sensor to focus on infinity. Conversely, wide angle lens would need to be really close to the film plane/sensor to focus on infinity.
Lens designers soon figured out a pretty cool trick though: they could create a long effective focal length by putting a short focal length element at the front, and a (slightly weaker) negative element behind it. With the negative element, the light hit the film plane at exactly the same angle(s) as if it had been refracted by a long lens. Exaggerating a bit (or a lot), we get a substitution like the following:
Both lenses have he same effective focal length, but (obviously enough) the second one is physically quite a bit shorter -- it doesn't have to stick out the front of the camera nearly as far.
The doubled upper-line in the second design, however, brings us to our second point: chromatic aberration. The "inner" line represents blue light going through the lenses, and the "outer" line red light. Because of its shorter wavelength, blue light is always refracted (bent) more as it goes through a lens than red light is. Depending on the glass, however, the difference between the refraction of the red and blue light may be quite large or relatively small.
If we pick the right glass for the front versus the rear element, we can achieve roughly what's shown in the picture -- the amount of extra bending in the front element is exactly compensated by the amount of extra bending in the second element, so the red and blue light come into focus exactly together.
With a zoom lens, however, things don't work out quite that easily. To get a zoom lens, we take the second design, but move the rear element relative to the front element. In this case, if we move the front element forward, the blue light will have diverged less from the red when they enter the second element, and since there's no more room behind the second element, it'll be bent more -- as a result, instead of coming into focus exactly together, the blue light will end up "outside" the red light, which will show up in the picture as chromatic aberration.
Conversely, if the rear element is moved back closer to the sensor, the blue light will have diverged further away from the red light when it gets to the second element. Then, since the second element is closer to the sensor it won't converge with the red, so it'll end up still "inside" the red when it gets to the sensor -- again, chromatic aberration (but in the opposite direction).
If we left it at that, zoom lenses would all be pretty awful -- every change in focal length would give huge amounts of CA. To combat that, elements are grouped. Instead of just the front element and second element, with one compensating for the CA introduced by the other, you'd have two groups of elements, each of which compensates for its own CA, and moving the groups relative to each other doesn't change the CA at all.
It's still not that simple though. It's physically impossible for a group of elements to completely compensate for CA. An element always bends blue light by some angle that's greater than angle at which it bends red light. At best, if you put the elements really close together, you can get the red and blue light traveling very close together and almost parallel, but still slightly separated. If you bend them back toward each other, they're only going to converge at one exact distance; at any other distance, you're going to end up with CA in one direction or the other.
As already noted, however, with a zoom lens, the distances involved must change. What the lens designer is normally going to do is try to minimize the worst case CA. Doing that is pretty easy (at least in theory): he looks at the range through which the rear element moves, and figures out the angle that'll produce convergence at exactly the middle of that range. This way he's splitting things, so it'll get CA in one direction as the rear element moves closer to the sensor, and in the other direction as it moves farther away. Of course, it's not really just the rear element though -- he has to look at the combination of all the movements of all the element groups (and account for the dispersion introduced by each, of course).
Once he's figure out the range, however, he usually minimizes the worst case by splitting the difference -- optimizing for roughly the middle of the range, so it gets a little worse in each direction. The exception is a lens that's expected to be used primarily at one end or the other. In this case, it can make sense to optimize for approximately the expected usage range, and live with the fact that the worst case is going to be worse than it would really have to be.
Of course, this is also looking at only one of the several factors important to a lens design -- the designer also has to take into account (at least) coma, astigmatism, vignetting, distortion, and spherical aberration -- not to mention a few minor details like size, weight, cost, and simply being able to manufacture a real lens that works the way he's designed it to.