Paul
I had this problem with the E65 730d ((07). It felt like it was hesitant at pulling away from a rolling entry to a roundabout or exiting a junction - almost like the turbo wasn't spinning up (turbo lag) or a gigantic flat spot.
Now I realise that your is the V8 petrol but if the symptoms are similar get down to your BMW dealer and speak to their BEST technical guy and I mean TALK to him not relay messages via the service desk guy.
I do not know exactly what they did to mine but they took it away for about 90 mins and did something to either the G/box ecu or the engine ecu or maybe both!
However, it now pulls like a train and will actually hit 155+ on the clock whereas before it would only show 145. Acceleration if similar to my old 440 V8 Dodge Charger with 400Hp. (1970)
Another of my theories was that it wasn't dropping into first gear on stopping - remember the ecu remembers your driving style and will adapt to it. The guy that had it before you could have been a lazy chauffeur and in London all day!
My car now always drops into first and no flat spots or stalls on acceleration.
One negative is that I have lost about 2 mpg but with 600 miles to a tank of diesel who cares? My older E38 V8 only did around 300 per tank.....
Hugh
BTW where are you?