One problem related to steering wheel vibrate has been reported for the 2001 Ford Taurus. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2001 Ford Taurus based on all problems reported for the 2001 Taurus.
Bought used 2001 Taurus in Aug. Of 2002. On the test drive I noticed the car pulled to the left and there was vibration in the steering wheel. The dealer at no cost to me did a wheel alignment and wheel balance. I drove again and it was fine. Approximately 4500 miles later the steering wheel vibration returned and the car was again pulling slightly to the left. I took it in to the dealer again and was told that the likely cause of the vibration was that a wheel weight was lost, but had no explaination for the pulling. They rebalanced the wheels and rotated the tires. Again everything was fine until Nov. 2003 as I was driving I once again felt the vibration in the steering wheel and it was much more severe on cornering. I took it to an independent repair shop(nearest Ford dealer was 25 miles away). They found the left front tire to have a flat spot on the outer tread area(slipped belt) and both outer tie rod ends to be loose, the left one being extermely worn. They indicated to me that they have seen numerous problems with the continental oe tires not holding balance, having bad wear problems, etc. They installed two aftermarket, greasable tie rod ends and did a wheel alignment and rotation. At this point I have submitted the repair bill to a Ford dealer for possible reimbursment, however I am not holding my breath. My opinion is that continental tires are junk and Ford knows it. The Ford dealer indicated to me that they have had no othe problems like mine, a much different opinion than the independent garage. Also tie rod ends usually don't fail at 39k miles for no reason. I have a friend that has a 2002 Taurus with continental tires and has had to have them balanced several times due to steering wheel vibration.