My last car wash left terribly ugly hard water spots on my car (nautical blue) . I tried waxing the hood but they were still showing. I read online about using 50% vinegar mixture. Holy Batman! That method worked well! Have to rewax the car today however as the vinegar supposedly removes the old wax.
I wouldn't recommend using vinegar. It's acetic acid and -could- damage the paint. I've found just using water will remove the spots, then dry with a microfibre towel before it air dries. Some car soaps will stop water spotting as well. Cleaning with it should also remove the spots. Car soap is made so the pH (acidity/baseity - if that could be a word) is compatible with paints.
An acid bath consisting of distilled white vinegar is actually what pros use if they're certain that the water spots are mineral deposits. However, it's best to use the least aggressive product to get the job done. Claying or a polish with mild abrasive (or even chemicals like Nufinish) can usually remove water spots.