The recipe on rice packs I buy says rice should be boiled uncovered. Why is that? I tend to cover it while cooking as it lets me use much less power. Do I miss something taste-wise?
You can cook rice covered or uncovered, it will not impact the flavor. The amount of liquid you begin with, and your cooking time, could certainly be impacted. There are several methods for cooking rice (covered, uncovered, and both). If you are using pre- or par-cooked rice, the directions are likely just a finishing step, formulated so that you don't over-cook the product. You could still use a cover, but would likely need to keep a close eye on it or experiment a bit to get a result you like.
If the recipe did not require you to wash the rice, then it would explain a lot. Without washing the rice, you'll be getting a lot of excess starch in the grains, and boiling with a lid on would likely result in it foaming-over (usually making a mess).
Did the recipe specify to cover it after the water is absorbed, or not cover it al all? Typical instructions for cooking rice on the stove include covering the rice after it boils.
Apart from the other answers given, certain types of rice and lentils when being boiled, create a lot of froth and bubbles. When the vessel is closed, these bubbles do not break up easily, and they build up and spill over the vessel. They also sputter quite a lot and leave a mess over the stove top.