in the main moles are harmless, just ambling around underground, bothering no-one.
And they do good too, in soils which clog up. They aerate the soil with their channels, and can bring soils which have become over-compressed and lifeless back to life.
It tends not to be something that happens with peaty ground, but now I am back on southern clay, I am grateful to the moles for opening up our soils again after the wet winter, when any livestock tramping (or farm vehicles, come to that) can cause the soil to become compressed and airless. And if we don't get any uneaten hay cleared up promptly in spring, that too can choke the soil, and we are again grateful to see the moles coming in to open it up again.
We have to do a walk around the hay meadow before mowing, is all, and either remove mole hills or mark them so they don't get mown and incorporated in the hay. Not a huge problem if it's going to be hay, but if it is destined to be wrapped (or might have to be, Cornish weather being as it is), then it's crucial to not include soil in the cut.