2003 Mercury Sable Shaking when braking

My 2003 Mercury Sable has had recent vibration problems. At 70 mph, the car would vibrate. I noticed a flat area on one rear tire, and replaced all four tires, since they were all near minimum tread depth. This solved the high speed vibration, but I still have a shaking in the steering when I apply the brakes. I removed the front wheels and inspected the pads and rotors. The pads are less than half worn, and the rotors still appear smooth and are within.003" consistent thickness. Is this enough difference in thickness to cause a problem? Or is the problem elsewhere, possibly in the suspension?