I don't know what to do with the poorly painted parts, that might require more than polishing. Here is what I would do...
Wash
Clay
Polish (Poorboys SSR2.5 with a Porter Cable 7424 at Speed 6 with a Polishng Pad)
Seal/1st Coat (Poorboys Polish with sealant, Poorboys Polish with Carnuba, Poorboys EX Sealant or Poorboys EX-P)
Wax (Poorboys Natty's Paste Wax-Original, Blue or Red OR Pinnacle Souveran)
You can read other threads here for more information or check out...
http://www.detailcity.org
http://www.poorboysworld.com
http://www.pinnaclewax.com
Good Luck