Problem: Front end vibration under braking.
Cause: Usually the control arm bushings are beginning to fail or the rotors have worn.
Description: A very common problem with the e28's. The bushings in the control arms tend to wear out pretty quick, causing the car to vibrate violently when braking at high speeds. The upper control arms have always been more noticeable(to me) when braking because they tend to "thunk" and move the entire shock assembly every time enough brake pressure is applied - While the lower control arms have always had the distinct vibration quality.
Typically, if the control arms are in healthy shape, then your next suspect would be the brake rotors being uneven/warped.
How do I know?: Throw that car in the air with your front wheels off the ground. Inspect the control arms to make sure they are in good condition. You can always get a firm hand on them and see if there is any type of movement, if there is, you found the weakest link. You can also take your problematic wheel and move it from side to side with a good amount of force, the troublematic arm is usually noticeable with movement (CAREFUL! Make sure the car is securely lifted!) Talk to a parts pimp about ordering from an assortment of control arms (poly filled or no).
If your control arms are good, then take a look at your brakes.
Check your brake rotors for heavy "pitting" -- where the rotors have developed heavy grooves are are no longer a nice smooth piece of metal. Also, if you have replaced the rotors recently and did not replace the pads, this problem can arise again quite quickly and is harder to identify because "I've already replaced the rotors." Yes, they were replaced, but the pads were grooved as well and will quickly re-groove your new rotors.
Sometimes a rotor can because even slightly worn and will cause vibration problems but still "look" good. I would check, recheck, and triple check to make sure that the control arms are not the problem then go ahead and assume it's the rotors.