rberns, I think your problem occurs for 2 reasons. First, you have a dark color car which shows even the slightest discoloration. Secondly, I would be willing to bet you have hard water in your area.
Try this: After the rinse, sheet the water off quickly, then spray the whole car down with detail spray, again as quickly as you can. Finally, use an Adams Great White Drying Towel on the car.
Another more expensive solution would be to install a hard water filter in your garage. This would totally eliminate water spots.
As always, keep a good coat of sealant/wax on the car. This too will help.
Good luck and let us know what finally works for ya.
Ron