Help: gray spots on white paint

[Z chick]

I've owned my PW Z for almost 2 months now, and since the time of purchase, I've washed it twice, so my car has never been incredibly dirty. The fender areas are usually the dirtiest places on the entire vehicle from dirt splash. My wash removed the dirt, but there are still gray spots that don't come off! The paint is still smooth over these gray spots, and there are no raised edges. I also don't have any swirl marks yet.

How do I remove these ugly gray spots?? I tried Meguiar's polish and it doesn't work.