Put put put put put put!

sounds like worn engine mounts, or trannys on the way out,, mine did a similar thing,, but was the tranny, when I stepped on the clutch it was quite ,released clutch at say a light it got noisy, on you car check facing front of car with car off, right in front of the rad you'll see the hydraulic tube goto the tranny kind of to you left a bit, right where that rubber boot is theres a fork under that rubber, with car off does this slop around? when you touch it with your hand? there's a spring in there that that fork clips onto that likes to wear out. when it gets soft it will make noise,, because the forks wobbling around and not tight and if really noisey change out your throw out bearing,, good luck.. hope this helps

try a simple fix of putting injector cleaner in the tank to clean the injectors
check for any loose body screws and panels

Sounds like a fuel filter or fuel sencer or maybe just a good tuneup

my 2000 mustang 3.8 also had a bad vibration. after many trial and errors we replaced the harmonic balancer..not too hard but requires the "special" tools...and you have to buy it from the manufacturer. my car ran like a dream.

bad ujoints

Pull the wheels off. Remove the 2 caliper bolts holding the caliper on. Pull out the old pads, put the new pads in with a little bit of antisqueal (silicone) on the back of the pads, then reinstall calipers. Make sure you put lock tight on the caliper bolts to keep them from vibrating out!

while driving at higher speeds you may not notice a sound as much as when you are drivng in reverse as you usually drive slower in reverse. This leads me to think that the rattling can be caused by a loose protective plate under the car. When a load is put on the engine, it tends to vibrate more this vibration can cause a lose plate to rattle more. This is the cheap answer. That is if you are definitely sure the sound is coming from under the vehicle. Otherwise, you may have a crank shaft problem or a seal in the bottom half of the motor could be bad. You may want to crawl under the car and try to shake some of those plates underneath. If none of them are loose take the car to BMW it shouldn't cast anything for them to look at it unless they have to hook it up to the computer.
Please remember that if you intend to climb crawl under your car, you must make sure that your car is properly supported to prevent serious injury. Also, if your driving with a loose plate, it could easily fly off while driving or if you hit a bump. This could cause serious damage to your vehicle. Also, please check you oil levels and make sure you do not have an oil pressure light coming on when you hear this noise.

i would be inclined to agree with the AAA man if you can find the fuse box have a look for any blown fuses hope this helps regards Jim

There is often one screw on the drum that holds it to the axle shaft flange. Try banging the drum with a big f'ing hammer (Technical term, not making it up) a few times to loosen it up a bit.