A shallow pond is going to have a higher percentage of water that supports weed growth. Not optimal, but you can work with that.

A shallow pond is also going to be hotter in the summer. Hotter water is less capable of holding dissolved oxygen. This puts your fish at risk of a fish kill. Once again, not optimal, but you can work with that.

Do you have AC electricity available at/near the pond? Reliable aeration would probably be a big plus for your pond.

If you stocked fatheads two years ago, it should be packed with them. Are you seeing minnows in the pond?