Your Koi may be doing some of the damage. They are notorious for chewing up pond plants. You may have a critter trying to catch the fish as well. With limited info, it is hard to be specific but the torn piece laying on top seems to indicate an attack from outside the pond. The attack may be on the fish rather than the plants if the fish use the plants to hide.

Herons and raccoons are the first to come to mind.

More detail about the pond would be helpful.

Hail damage

Sdavis, except for the small amount of damage I agree. It does look like the kind of tears a hailstone would give. Since hail doesn't keep coming back, I would think of someone throwing stones in the pond.

Are there any kids around who would do that kind of mischief?

That's what mine looked like when the raccoons used to visit. I put a "cat scat" ultrasonic pest repeller pointing down towards the water line and they don't visit anymore.

I am seeing this on the edges and figured the birds had discovered them.

Try feeding your fish more. It looks like mine when I don't feed them enough they get hungry and will eat holes in your water lilies leaves. Koi eat water lilies. If You let them keep eating them they will completely kill them. I've seen this many times in my water gardening business.

Here is a link that might be useful: makemoneygardening.org