I've never seen anything quite like this. I am tending to agree with CPS that it may be stearic acid forming on the soap sides. I use stearic acid as a additive in 2 recipes that are normally softer since they are high conditioning recipes. I never use over 3 to 4% though. Interesting. It it were lye on the outside touching your tongue quickly and rinsing with vinegar or water would test that out. "Hey Mikey, wanna lick my soap? I don't wanna try it; you try it!" Just kidding about Mikey.
I use to get spots like this too!! What do you line your molds with? I use to use wax paper, but switched to plastic (cling) wrap, and haven't had the problem since!