Since I got my information from my wife who is very seldom wrong, I decided to research it further.
From the "Home & Garden TV" web-site:
Remove Lime Deposits
To remove lime deposits from shower heads and faucets, remove the hardware and soak in vinegar to dissolve the deposits. This method also works for cleaning rust off tools.
From the "On the House" web-site:
How to Remove Lime Buildup on Your Faucet
Are you tired of scrubbing for hours to remove that white, gritty lime buildup on your kitchen or bathroom faucet? Whatever you do, don't use scouring powder. Although it will make quick work of those nasty mineral salts, scouring powder will scratch chrome or brass. We have a tip that will make cleaning this unbelievably easy -- and without the worry of scratches: Soak a cotton or paper towel in a bowl of white vinegar. Wrap the wet towel around the fixture and let it remain in place for at least an hour. Next, remove the towel from the faucet and use it to gently whisk away vinegar-softened water marks. Finally, rinse with clear water and buff dry with a clean soft towel. Next, sit back and enjoy the shiny example of your own, terrific handiwork. And that's the On The House tip for today.
From another site:
33. To remove lime coating on your tea kettle; add vinegar to the water and let stand overnight.
There were lots more like this, but I ran out of patience.
I still think I would try the vinegar on at least one spot.
Charles