What is eating the planted corn in my garden?

probably squirrels. They know those little green flags all mark a corn kernel and will pull them up as fast as they can. I've known of people to spread corn (feed corn) on top of the ground in the same are so the squirrels eat that instead of pulling up the shoots. In a week or so more the seed corn will have disappeared into the root system and they wont pull them up anymore.

There are little holes about the size of a nickel at each kernel. I thought a squirrel would make a bigger hole. We put out poison for mice and rats.

Voles will cause the biggest problem with seeds that are in the ground – mainly corn and soybeans.

Give them something to eat for the time being, until the crops gets past a stage where they can survive without significant damage from vole feeding. Cracked corn, soybeans, wheat and rye all are good alternative baits.

I have heard of crows pulling up the corn sprouts, but never had that problem.

Black birds...did you get treated seed? If not, black birds will murder your corn

Eta - do you see any kind of tracks left behind? Bird feet, squirrel feet, etc?

Possibly black birds? How deep are you planting it?

Mole crickets