I just want to say all the above answers are misleading!

I renewed my car 3 months late (May 2013) and the fine is only 500 QR. You have a grace period of 45 days.

You can see the captain if you have a genuine reason (example vacation, parts not available etc), but he may ask you to come back the next day or see another officer in another shift. You can save time by just paying the fine.