| My needles also do this but never given me any concerns or problems so far. (2002 MINI owned last 2 years).
From MINI2 FAQ :-
Why does my speedometer shake or rattle on start up? Short Answer:
It's re-zeroing itself. It only needs to re-zero after a reset, and this happens either a) when you remove the battery, or b) if you turn the ignition to position 2 more than a minute and a half after ignition off.
Long Answer:
The mechanical backstop for the stepper motor that drives the speedo needle is a few degrees below the visible zero mark on the display. Before the instrument packs leave the factory, the needles are optically aligned with the zero mark, and the difference in angle between the backstop and the zero mark is written into the memory of the instrument pack. On a reset, the needle is driven backwards into the backstop, and then forwards by the calibrated angle to the zero mark. The needle will shake as long as the motor is driving back against the backstop. Because the calibration varies between cars, the amount of time (and severity) of the shaking will also vary, and some cars audibly rattle.
Short conclusion to the long answer: It's a quirk, but go ahead and complain if you think it's really bad.  | 
