I had this problem too.
After scrubbing with paper towel I gave up and grabbed a green scrubby pad used for dishes and it works perfect! I was worried it would scratch the glass but if your careful it shouldn't cause any damage. At least I didn't see any when I used it.
To try and prevent, I noticed when I started over filtering the water it wasn't as bad. We have a sink filter and I put the water in a brita filter jug. Or you could just buy "spring" water from the store. I'm not sure if this helps anything but I'm sure others have better experiences.