Although it might all look the same to the untrained eye, the truth is that the quality of the water which flows from your tap can vary wildly from place to place. This isn't such a big deal if you're cleaning countertops or flooring, but since glass shows every little imperfection it will be very apparent if any impurities are involved in the process. Since many people dilute glass cleaner with water this can have a major impact on how your glass surfaces look after a good cleaning. Hard water, in particular has a higher concentration of dissolved minerals such as magnesium and calcium, which will almost definitely result in an unsightly, streaky mess when combined with your cleaner.
Instead of diluting glass cleaner using water from the tap, consider using distilled water. It doesn't have all the minerals in it that can be present in tap water, so it won't leave behind any streaky deposits on your bathroom mirror. Unless you need very large quantities, distilled water is relatively inexpensive and easy enough to purchase from the local grocery store. If you're really pinching pennies you can actually whip up a batch from the comfort of your own home!