If your corned beef hash isn't crisping up, it's probably because you didn't preheat the pan. Next time, make sure the pan is hot before adding the hash. This trick will help create a crispy exterior. I recommend using cast iron or nonstick skillets for this.
Soggy corned beef hash might be due to overmixing or using too much grease. Cook the hash on medium-high heat in a skillet until browned and crispy, and drain any excess grease before serving.