as someone who painted aircraft for more than 4 years, I can tell you that leaving dirt on a surface that's to be painted is silly! The paint is FAR more likely to flake and peel than if you were to prepare the surface properly.
my advice, get an air- or electric-powered sander, some 40-grit sandpaper, and go to town.. give everything a nice rough/smooth finish.. by that I mean that if you look at it, it appears rough, but when touching it, you can barely feel the grit.
once you've done that, hit it with a primer that's appropriate for the type of paint that you want to use - use a 'dust coat" as the initial application - like the name implies, you're just putting a dusting of primer on at first. Using the dust coat will ensure that - if you missed anything in sanding - and spots on the surface that aren't adequately prepared will be good to go.
once the dust coat dries, hit the surface at least twice more until you've achieved complete coverage (best bet - choose a primer that doesn't have a similar color to the surface you're painting... once you only see primer color, you're done!).. THEN put the paint you want people to see on.
I don't know if you're looking for an easy fix, but I hope you're not... because easy leads to messy, and that's the last thing we want on the playa.