This page was originally hosted here: http://cbsgi1.bu.edu/bmw/bmw_new.html. But that site has gone down so I'm hosting these pages here.
Front end shimmy is a common problem with some BMW's. Most complaints are from ???? 5 series, and ???? 3 series. The fix seems to be a bit of black magic involving either/or: pads/rotors and suspension parts like control arm bushings. Here are some anecdotes from the bmw mailing list:

Date: Fri, 3 Dec 93 12:13:46 PST
From: "John Coffin" 
To: bmw@balltown.cma.com
Subject: Re: Front End Shimmy ..
Original-To: bmw

In-Reply-To: WRPYR:bmw-request@balltown.cma.com's message of 12-03-93 11:30

>A note: They only put weights on the inside of the wheels ..
>        The dealer put's em on BOTH sides ...

While putting weights on only one side of the wheels usually works fine I
have noticed that in some situations (the reason remains a mystery to me) the
only way to get some cars to stop the wobble at some speeds (if it's all speeds
the wheels are not balanced correctly) is to put the weights on both sides. 
This seems especially true if the wheels have any nicks in them.

One way I have seen the weights on one side work is to have a strobe balance. 
A strobe balance is done by spinning the wheel on the car and using a strobe
and variable weight set on the wheel to balance it while it's turning.  I've
haven't seen one in a while (it's an old idea).  The last place was the
Porsche shop I worked at.


====
John Coffin
>From: "Kuzma, Joseph P." 
To: bmw-request 
Subject: Re: Front End Shimmy ..
Date: Fri, 03 Dec 93 15:28:00 est
Encoding: 49 TEXT
X-Mailer: Microsoft Mail V3.0


One of my cars had a front-end shimmy when it went 55-60mph.  It was very 
annoying, and the car went in and out of the shop so many times I don't care 
to remember.  This was on a new car, just purchased.  It escalated to the 
point of invoking the local lemon laws on the car, and contacting the 
manufacturer.  The manufacturer contacted me (after I sent out my letter 
requesting full refund of my vehicle, with copies of all the repair receipts 
and failed attempts at getting rid of the shimmy) and recommended that I get 
a full-on-the-car balance.  This is a process where they balance the wheels 
on the car (sounds like your strobe method of balancing).  The manufacturer 
told me that this is something that they are now considering requireing in 
all their authorized shops due to the way the cars are made.  (Something 
about striking a balance between sporty and luxury ride).  Anyhow, they did 
this to my car and the shimmy went away!  But, unfrotunately for me, 
everytime I do anything with my tires/wheels I need another on-the-car 
balance which is not cheap and hard to find.

BTW: The manufacturer was Honda
 ----------

Date: 3 Dec 1993 16:08:05 U
From: "Kinports Brian" 
Subject: Re: Front End Shimmy
To: "ZBMR List" 

On the Car Balancing  

My experience with some cars particularly 320i's is that a 1/4 oz uncertainty
in most common balancing equipment can contribute to front-end shimmy.  On the
car balancers solve this problem because they are sometimes more accurate and
the following theory:  The rotor and hub assembly can contribute to an
unbalance of the rotating assembly including the wheel.  To carry this further,
the wheel/tire must be mounted in exactly the same position on the hub every
time or the balanced assembly will change.  

Brian

From: welty@balltown.cma.com (richard welty)
To: bmw@balltown.cma.com
In-Reply-To: "Kinports Brian"'s message of 3 Dec 1993 16:08:05 U <9312032104.AA04422@balltown.cma.com>
Subject: Front End Shimmy

> The rotor and hub assembly can contribute to an
>unbalance of the rotating assembly including the wheel.  To carry this further,
>the wheel/tire must be mounted in exactly the same position on the hub every
>time or the balanced assembly will change.  

speaking as someone who changes tires too damn often every year, this
is for me a good reason not to bother with on-hub balancers.  a further
reason not to bother with them is that i know two people who are good
enough with a quality spin balancer that i _never_ have a problem with
wheel balance provided that the wheels are round and true, leading me
to the conclusion that on car wheel balancing is just a scam.

cheers,

You raised a good point about wheels being true enough to balance.  Tires can
also be out of round and cause an inability to balance correctly.  

I also agree that changing tires too often is a real bother.  I run my street
car at various driving schools in the southeast (Sebring, Road Atlanta, etc.)
and change to race wheels/tires on a very regular basis.  I have always lived
with the little 45-60 MPH shimmy in my 2002.  

Happy Motoring,
Brian


On the Car Balancing  

My experience with some cars particularly 320i's is that a 1/4 oz uncertainty
in most common balancing equipment can contribute to front-end shimmy.  On the
car balancers solve this problem because they are sometimes more accurate and
the following theory:  The rotor and hub assembly can contribute to an
unbalance of the rotating assembly including the wheel.  To carry this further,
the wheel/tire must be mounted in exactly the same position on the hub every
time or the balanced assembly will change.  

Brian