Why does asparagus microwave so fast?
A couple things... Yes the microwaves excite polar molecules. Water happens to be a very common polar molecule. So the first thing I would expect would make a major difference would be the ratio of polar to non-polar molecules or the percentage of water in most cases. Asparagus has a  high percentage of water at roughly 93%. Peas on the other hand have about 79%. Potatoes are also about 79%. Assuming to objects of the same shape and density, the one with more water will likely heat up quicker.
The second thing to consider is the shape (or more importantly the surface area). A potato is much thicker, and the surface of the potato will absorb most of the microwaves, causing the inside to stay cooler, much longer. The heating will be much less efficient and effective than heating the asparagus.
Edit: As Jefromi pointed out, there is also the fact that asparagus is always going to cook faster than a potato in absolutely EVERY cooking method.