I have a 64 Malibu. I noticed some rust forming on the inside part of the driver's door, near the bottom. I ran my hand on the bottom inside portion of the door and found a couple of soft spots. Surprisingly, you can't see it from the outside.

What is the best approach? Patch it? POR? New skin? New shell?

Thanks

Its rusting from the INSIDE OUT. The ONLY cure for that type of rust is removal.
The best bet would be to replace the entire door skin. This way you can remove any rusted areas and coat the inside of the door shell with primer to prevent future rust.
Install a new door skin using adhesive with NO welding and it will outlast you