Try using a Mr. Clean Magic Eraser.

Maybe vinegar solution? Or, use a microfiber cloth, spritzing with water only.

spray on straight vinegar and let it sit for several minutes then wipe or scrape off.

White vinegar and scrape works for us, too.

3 words for you: Bar Keepers Friend. Here's my original post about it.

+++++++++++

I've tried everything over the years. Never had much luck with vinegar, fabric sheets, oven cleaner, and all the other suggestions. They kind of work, but not to my satisfaction. Plus, many are toxic. That's not how I'm going to go out.

Then I happened upon a random posting online where a guy methodically tested all these different solutions in a controlled environment -- side by side in his shower. See URL below.

Without a doubt, BARKEEPERS FRIEND is your solution. I've used it for several years since and it works wonders. My wife uses it to clean our kitchen sink and other surfaces. It's cheap and available everywhere. It doesn't scratch. Leaves no film. And isn't toxic like all those products that need "good ventilation." It's got oxilic acide or something like that. No scrubbing. Apply liquid or power (with water) with a sponge, do 3-4 circles, and wipe off. No sweat and instant gratification.

A little car wax after cleaning and you're all set. Trust me. You can thank me later by verifying my suggestion...

http://www.themanlyhousekeeper.com/2011/03/11/solved-soap-scum-and-hard-water-stains/
http://en.wikipedia.org/wiki/Bar_Keepers_Friend
http://www.barkeepersfriend.com/