Pearl White paint with tiny dots of Rust

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There are different types of clay that are more aggressive than others. Some are harder and don't clean the surface as much as some of the softer and more aggressive clays. The softer clays are a little harder to use which is why the consumer types are harder. All of those spots should come off with either some clay or with polishing. Try some Meguiar's Scratch X or some other type of polish and they should come off.