My dog scratched up part of our interior wall next to a door. He tore off the molding around the door and also scratched some of the drywall off. There are no holes in the drywall, but there are some scratches that go fairly deep into the drywall. The area I am talking about is probably 3 inches wide and 3 ft tall. Part of that area will be covered up by the molding. Can I use spackle to repair this or is it better to just cut the damaged drywall out and replace it?
I'd use actual joint compound. I'm not sure what you're referring to with "spackle", but in my experience it's a very fluffy, soft product. Get some topping or repair compound and apply it twice (it'll shrink a bit), then sand lightly. Prime and paint.
It's not necessary to replace the panel or use joint tape for surface scratches, even if they're through the paper.