Hard water spots can be tricky to fix. (Sorry new here researching an issue with the wifes car, couldn't resist the detailing section). Depending on how long they've been on the car they can be cleaned with the vinegar trick, usually within a few days at the absolute most. After that it will require anywhere from a light to aggressive polish with a rotary or DA, I suggest Meguiars M105 and an Orange LC pad for the aggressive stuff, or M205 and a White LC pad for the lighter stuff. If you are not making head way with the M105 then it may either require a wool pad (then continue with proper polishing technique to restore the gloss), or even as far as wet sanding. Though I only advise wet sanding in the absolute extreme. It should also be done by a pro only as it can be easily hosed up, and you can be to primer or bar metal in seconds.
More info check out autogeekonline.net or autopia.org great detailing sites and I've learned a lot from there too.