is the overdrive automatically on when i start the car? It seems the o/d off light only goes off if I push the o'd button on the gearshift

Ippy, overdrive should not be engaged when you first get in the car. It's not something that you should be engaged unless the driver engages it manually. As far as knowing if it is a design flaw I would recommend going to a Mazda dealer and asking the service department.

Thank you very much for your help. I agree that the o/d should old come on if I push the button/

I know this is an old question but i have recently purchased a 2002 and the overdrive override light is never on when starting it and only comes on when I push the button. Are you saying it should be the opposite?

Od should always be on for normal driving like level drives except under steep grades check owners manual.