I found this list of urls with information about cleaning tiles. You might find your answer there. I hate tile myself, been there done that. It's more trouble than it's worth in beauty. If you ever get the marks off, a quick wipe down with a dry towel after your shower should prevent the spots from forming again.

I removed water spots from my shower faucets by soaking a towel in vinegar, don't remember if it was full strength or weakened with water. I wrapped the towel around the faucet and two treatments removed them. You might try a small area first with with an old towel soaked in half water and half vinegar.

Here is a link that might be useful: water spots

I have the same problem with my shower floor. Did you ever find a solution?