Rubbing compound will probably strip the paint. Patience and mild cleaners will probably be less invasive.

I got good results on newer paint and "texas pinstripes" using Meguiar's Clear Coat body scrub to get rid of scratches in the clear coat. It's a mild abrasive cleanser.

You might try a household Heloise trick of soaking a paper towel with vinegar (or vinegar-water solution) and letting the saturated towel adhere to the side of the car. That keeps the mild acid in contact with the hard-water stained surface longer so a less harsh chemical can work over a longer period. Keep the towel moist with a spray bottle, if needed. That's a recommendation for cleaning bathrooms, not 30 year-old car paint, though. It worked in my shower where Lime-Away wouldn't and abrasive cleansers required too much effort or would scratch the surfaces.