The stains being left on your glass are from minerals in the water. Even filtered water will leave some water spots. If your water filter doesn't filter chlorine it's still not safe to mist with.
The very best water to mist with is Distilled. Distilled water is totally pure, there are no minerals in it to stain the glass. Keep in mind, you don't want your animals to soak in distilled water because it could rob them of vitamins and minerals, but it's perfectly safe to mist them with it. I mist all of my tanks with distilled water. I buy it for 85 cents per gallon at my local grocery store.