That is very strange. Is this an exterior masonry wall? Did you prime or seal the wall before painting? It's hard to say exactly what is going on. I'm thinking it might be the emulsifiers separating from the base. This can happen with exterior paint when the weather is cold and very humid during or right after application.
Have you tried to wash the affected areas with plain water and a soft cloth? Do they go away then reappear?
What you need to do is make sure there isn't excessive moisture in the wall, look for water damage. Now you need to prime and repaint.