I have well water. Well was drilled into limestone bluff. Needless to say there is heavy lime deposits left on everything. Dishes especially glassware gets a cloudy film when run through the dishwasher. I use straight vinegar added to the dishwasher right before the rinse cycle about once a week. Everything comes out sparkling clean. I also clean the bathroom tub, sink and shower with vinegar. It's the only thing I've found to cut through the lime quickly and easily. I like that it has no added chemicals too!
You might be careful using vinegar with some metals. The acid in the vinegar can eat through the metal. I've had no problem with stainless steel though.
I also used to work at a Sonic Drive-In long, long ago. We used a mixture of vinegar and water back then to cut through the grease on the counter tops and wash the windows. Worked great!
Some people who have heavy lime or other minerals in their water swear by using a few tiny pebbles in their tea ketters. Have you tried this?
And Sue, thanks for posting the Wikipedia link!