This problem has been seen a number of times. Various methods for addressing it have been discovered, though none (except the last) have worked in all situations.
Understand that the problem might be mechanical, with a failing door lock actuator being the prime culprit. Also loose/corroded wiring cannot be ruled out.
(1) "Resynchronizing" the door locks.
Door locking is processed by the BCU (body control unit) computer. As with power window operations, the BCU may become "confused" as to the state of the individual door locks.
You can try to synchronize the door locks and the BCU by manually locking both doors. Make sure the key is in the ignition and is turned to position 1. Hold down the door lock switch for about 10 seconds and release. Switch off the ignition and back on again. Try to see if the switch now operates the doors properly.
(2) Disconnecting the battery
Some folks have addressed this problem by disconnecting the battery. Note that you will zero-out your trip odometer, clock, and average speed/mpg values by doing this.
Remove the cables from the battery starting with the negative terminal. Remove the positive cable. Wait for about 5 minutes or so, then reconnect the cables.
Try the locks again. If the problem persists, try resynchronizing again.
(3) Dealer Service
If I were to guess reason for your MINIs behavior, I'd put my money on the actuator. If you are outside of your 4-year, 48,000 mile warranty, figure depending on your MINI dealer's labor rate. This is just a guess so don't hold me to this figure.
Hope this helps,
