I know the kind of trim you are referring to, the Olds Starfire trim is some rare stuff, I used to have a 62 convertible. You want to be extra careful with it, if you are looking to attempt some dent removals or straightening, try light mallet tapping on a scrap piece of aluminum first, this will give you an idea of the kind of force needed, patience, patience and more patience! For buffing or polishing, I would try Mother's Alum. Polish. Good Luck!

If is not beat up, but only discolored or tarnished, then try some Eagle One brand wadding polish available at Wal-Mart and most auto stores and do some rubbin.