What I have found to work well is using a clay bar to clean the surface thoroughly.....The clay will remove the light spots, but you'll need a buffer and some compound to get the "deep" spots...
I would wash thoroughly then clay bar, polish, and wax. I usually have good results that way but a buffer with a light compound will be needed to get the tough ones. Here is a link http://www.autogeekonline.net/ that is full of detailing info. a lot of pro's on there It is ridiculous the way some of the cars look before and after.