The older leaves of my heuchies are riddled with ugly vaguely oval shaped holes. What could be making these holes?
It's hard to say without a picture, but holes in the leaves sound like beetle damage. Heuchera have very few pests, but the black vine weevil and the strawberry root weevil will occasionally eat holes in the leaves.
Vine weevil mouth parts work in such a fashion that they are only able to feed on leaf margins - you will see telltale notching of the leaf edges but never holes in the center of the leaf. Vine weevil larvae are much more likely to bother heucheras by feeding on the roots. Holes in the center of the leaf sounds more like slugs or snails. Or possibly some sort of caterpillar-type larvae. I'd bait for slugs first but if you use Sluggo Plus, you can kill two birds (or multiple leaf snacking insects :-)) with one stone.