My advice is, I hate to say it, to pay the ticket and try to forget about it. If you fight it, you may end up losing even more money, and you'll be fuming every time you deal with it. Let it go, and focus on stuff you can control.
Oh, and for future constabulatory entanglements, I find that you always get away with just a warning by starting with: "Sir, is that doughnut powder on your mustache?". They love that.