Being built in the late 40's, it would be plaster. If that were the case, the surface mold would just need to be wiped off with a chlorine/water mixture. It would be odd if moisture permeated the plaster and did no damage to the wall.
An easy way to check would be to scope the walls in a few spots. You can cut a hole the size of a pencil diameter and insert this scope into the wall cavity. It has a light on the end of a fiber optic 36" wand the bends.
I use one to do inspections for problems just like this.