Don't know if this is relevant to your problem ..
I used to have 'black' (whites on neg - opposite to yours) spots on prints when I used tap water and Rodinal combination. Not always but quite often to be a PITA.
When I used the same tap water for other developers like D76 or XTol no spots whatsoever.
So, maybe there is something about Rodinal and 'impure' water.
Since then I use demineralised water to mix and dilute all my developers .. problem dissapeared.