Do you have antilock brakes? if not have you locked your tires in a panic stop? if you have any sort of a flat spot on your front tires the steering wheel will move back and forth even at about 20 miles per hour depending on how bad or how many spots you have. if it is this problem it should be no big deal it just gets very annoying very fast trust me. hope that helps

    another thing i have read somewhere that the contour and all of its sisters cousins etc. have very very sensitive steering and track this i have also found to be a problem on my 99 contour se sport v6 mtx. if i have the slightest alignment problem it starts to shake almost violently the higher your speed.(at 70mph i thought the thing was going to shake itself to death)
    good luck with your solution hunting