Front end shimmy upon braking

This is a two-part answer: first, these cars' suspension was intentionally designed to be responsive and nimble, unlike large American sedans which allow heavy weight to rest on the front wheels. As a light suspension, it is more prone to transmitting vibrations through the steering wheel. In the 3-series and 5-series, these vibrations are caused by deteriorating components in the suspension. As these various components wear, the evidence of their wear becomes apparent through vibrations in the steering wheel most noticeably upon braking, and particularly between 50-65 mph (80-105kph). Second, the other half of the problem rests with the material used in the brake pads and how it interacts with the rotors. In the mid-80's, asbestos was outlawed in the USA. After the BMWs of that era had already been designed and produced, BMW had to search for a semi-metallic pad for replacement parts (scheduled maintenance), because they couldn't sell the asbestos pads once the asbestos law went into effect. The asbestos pads were originally selected because they were able to generate acceptable levels of heat, while it was much more difficult to reach similar specifications with semi-metallic pads. In time, the additional heat generated caused the rotors to warp. During this period, BMW issued many "updates". They used a number of rotor and pad manufacturers, including Textar and Jurid. They did this until they felt they got the proper pad-rotor combination. It was fairly common for dealerships to replace set after set of warped rotors and ruined pads in some customers' cars (dealers can fish for an answer, too). The rotors were often replaced free under the 12-month parts warranty. Unfortunately, although this problem was known while the E34 and E36 were still in development, these cars exhibit the same problem to a lesser degree. The E46 and E39 have been reported to have the same susceptibility to shimmies, but the underlying suspension components are stronger that older models. Again, replacing brakes with new ones won't solve the problem (for too long) unless the suspension is in good shape.