The good money says that they're digging for something to eat, and it definitely could be grubs. My suggestion would be to find another section of turf and pull up a section. If there's an abundance of white grubs then you can figure that's the problem. If you've already put down grub control over the whole yard then your search may be inconclusive. Grubs are nasty; by the time you can see the damage to the lawn you've got serious problems.
If you don't have any more crows feeding, I'd recommend seeding those areas. If it's just a small area you could use Patchmaster or a similar product.Where I live it's almost too late in the season, but if you have some warm weather still in store you should be in good shape.
Hope that helps.