I am a new 06 mini owner. I have noticed that when I am trying to rev my car while sitting at a light. If I give car quick peddle rev. The engine hesitates a little before it catches up with the peddle

 

This is normal to an extent. The stock flywheel is too heavy for the engine size, and the throttle is drive-by-wire, it is not perfect. However, a good tune will improve the throttle responce. I have not gotten a tune, but others speak highly of RMW tunes.