Went to remove the rear license plate on my '06 X3 and found the screws holding the plate to the mount were turning without loosening. I was finally able to get 3 of 4 off. At that point I removed the mount by removing the 2 torx head screws that hold it to the rear hatch sheet metal. The problem was caused by the screws slightly rusting to the nuts that are in turn held in place by rubber moldings. Of course, if there is much resistance as there was by a little corrosion between nut and bolt, the nuts simply turn in the rubber mount. The local BMW dealer's parts person said they keep them in stock because many people have the same problem that I had.
Remove the 4 screws holding the plate on and coat them with a little amount of anti-seize compound (readily available at any auto parts store). This will allow them to come out easily in the future and prevent the nuts from turning in the rubber mount. This is especially important if you live in the northeast, ie road salt country.

Jim in CO