My 525i has recently developed similar symptoms. i.e. gearbox goes into safe mode. If you stop the car and restart the engine it clears the fault and the car drives normally for a while.
This fault only happens when I’m stationary or at low speeds. On a few occasions the ABS light has come on, together with the yellow warning triangle. When this happens, the Speedo stops working ( not the rev counter) However if you continue driving after a while the ABS warning lights goes off together with the triangle and the Speedo starts working again. The gearbox light remains on and the car stays in safe mode.
One other point I’ve noticed is that, if you stop and clear the fault by restarting the engine and continue on, the fault will comeback more quickly each time.
Looking through various entries, it sounds like most models of BMW suffer from this fault. Has anybody any ideas?