Since caterpillars eat a lot, they also produce a lot of droppings (called frass). You'll need to clean out the caterpillar's housing regularly. When the caterpillar is on its food plant, it's a fairly easy process. Just remove the food plant and the caterpillar, and let it continue munching away while you clean house. Make sure you clean out the small jar holding the food plant, too.
If conditions become too moist in the housing, you may discover fungus forming in the soil layer. When that happens, be sure to remove the soil completely and replace it.