Vinegar does work, sometimes better than supermarket cleaners that claim the same removal properties. Best bet is to squirt the vinegar & give it a quick wipe over, then come back later & remove with a scraper. This usually works with light hard water removal.
If this doesn't work, you may have to go the MDR route which is more time consuming. Shower doors & enclosures can also be cleaned with a cut half lemon. Like any chemical removal - let the chemical do its work, 20 minutes or so.
There are quite a few products out there especially formulated for window cleaners. Educating yourself on types of glass & equipment to remove hard water stains goes a long way.