[RWebb]

last pic looks like marks on top of paint

stick a foam pad on a random orbit sander if you don't own a D/A buffer (and only pros or crazy people need to...)

use a polishing or cutting compound of your choice

I am no artist and deal with my potential klutziness by using the Meguairs compound in the red bottle (red (maroon) = amateur line) - they call it a rubbing compound but it is more fine than what I done learnt was a rubbing compound in the South eons ago...