Dixie, I had a similar batch that looked identical to yours with spots appearing after a couple of days. The spots didn't get any bigger or smell off though I did end up chunking the soap out of an abundance of caution. Plus I didn't really like the scent or appearance of it even without the spots.
My best guess for the cause was some litsea EO that I used in an EO blend since I made other batches that day from the same ingredients. A little later, I was about to use the EO for some bath truffles and had poured it into a glass container. The sun was setting, and I noticed particulates floating and glinting in my container. It was a gift from a friend, and I'm not sure where they bought it. Of course, I failed to make note of the brand; however, it wasn't one I'd seen before.