First, there is of course no need to use just the generated fractal to create a landscape. We are free to take the landscape and then manually apply some change in altitude to various regions of it. So that gives us a mechanism for modifying the fractal's output.
As for what to do with that mechanism, the appearance of the Earth is in many ways an artifact of the system of crustal plates that make up its surface. The plates are mobile ("continental drift") and where two plates collide, the ground will buckle upwards and create mountain ranges, island chains, and land bridges. So if we could find some way to approximate the effect of this process, we could use it to add some realistic large-scale structure to the landscape.
My current thought is that if we can construct a network of random seams across the surface of the sphere, we can then simply increase the altitude of points that happen to be near the seams and the result should be distinctively Earthlike mountain ranges and island chains. I can even start out by using the current version of the fractal planet created using the sphere-halving algorithm, just to see if it works the way I hope.
Update: One nice potential angle for the future is that mountains also have a major effect on the climate of a region -- if mountains are between a section of land and the sea, then moisture evaporating from the sea and brought in on the prevailing winds will tend to rain out on the seaward side of the mountains, creating fertile areas on the seaward side and leaving a desert on the other side. So knowing from the start where the world's major mountain ranges are, we could add climate zones to either side and create more plausible deserts and temperate areas as well.
Further update: I suddenly realized -- this explains why the "slice the globe in half along random vectors" scheme I've been using up until now actually produces good-looking Earthlike planets to start with! It's because this method creates long, narrow wedges across the planet's surface, and these wedges approximate the shape of island ranges and narrow continents otherwise created by the plate tectonics process -- shapes that rarely get created by more traditional fractal subdivision. Oo.