Originally Posted by JCL

With the vehicle off the ground and properly supported on jack stands, get underneath and inspect all bushings. Each end of both the control arms (rear, front wheel) and tension struts (front, front wheel). See if anything moves when you lever on it. It may not, you may just see a tear in the bushing, or other signs of wear. There doesn't need to be much play to allow a shimmy under braking. The bushings come pressed in, you buy new control arms.