Could it be possible that those spots were there even before you purchased the vehicle, but were maybe concealed by a polish that was heavy with fillers?
I don't know about now, but years ago I tried some of the Simonize products but was not happy with the quality of the product. I also used to use a lot of the Turtle waxes but stopped using them because it was like trying to take cement off of paint. Have you tried using some of the
Meguiar's waxes? I use the Gold Class and am pretty happy with how easy it is to apply and remove and with how good it looks on my paint.