I got my BMW recently where the previous owner did not drive the car for a while not less than 2 month but noticed when accelerating black smoke was coming out of the exhaust should this make me worry
It could be a number of things.
If it is really a black smoke, it points to a fuel-rich mixture. Could be a problem with your fuel system or your Airflow and O2 sensors. Normally you should see an error code for most of this over OBD2.
If it is more of a blue-ish smoke, you could have a problem with oil leaking into the combustion chambers. Not unusual for BMW which where pushed while still cold.
Reference: Exhaust Color Diagnosis