I use vinegar, but not in the actual 'wash' water, instead in the 'rinse' water.
I have two buckets: one with hot soapy water (e.g. some dish detergent) for the actual washing. Then a bucket with clear hot water with a squirt of (distilled WHITE vinegar) in it, for the rinsing. Then I squeegee (sp??) it dry and use a lint-free old dish towel to completely wipe it dry. The vinegar helps it from drying with streaks.
I don't have a specific ratio, I just squirt some into the water, probably about 1 part vinegar to 2 or 3 parts water or so.
And yes, I use it on bathroom mirrors, too, have had no problems.