We have a lot of mole hills and runs in our yard. Last year my DH obsessed over them, anxiety spiking every time he saw a new one. I often would stomp them down in the morning and replace the sod before he would see them, just to keep him from having an anxiety attack.
When the chickens find them, they make a dust bath out of them, so that made the whole area look even worse.
This year, he is not nearly as anxious about them (other things have his attention right now) so the moles are having a field day, and so are the chickens.
In the spring, when the moles are making shallow runs, we are pretty good at using the "dispatch with shovel" method: You have to be able to recognize a fresh hill, and watch it for a couple minutes to see if they are working it right now. If so, walk softly back to the house to get your shovel.
Watch the ground movement to see which way they are working, and exactly where. If you can stomp down in back of them, and push the shovel down in front of them at the same time, you can pop them out of the ground in the shovel. (this works better with two people, in which case, you can each use a shovel) My DH got pretty accurate using a hatchet to chop them in the run. Very satisfying.
I think this works best in spring, or anytime the moles are working shallowly. In hot dry weather, when they go deep, and push up the huge mounds of dirt, I haven't found anything that works.
I read a blog by an organic gardener who said the moles do eat grubs, and aerate the soil. Just accept it and get on with your life, was his advice.
