Dear Forum
This is my first posting here. I am very grateful to be able to post here – I hope that with all the wisdom and experience around that there will be light at the end of the tunnel for me and my BMW.
My question concerns my BMW Touring (E46) 320i, M-Sport, Automatic, 2.171 ltr, 2003,  which I have had for around 6 months.
While driving at around 80 kmh, or sometimes below that speed – but not at all speeds – and while in “D”, the rpm fluctuates slightly. This is noticeable on the rev-counter, and I can also hear the engine making a “dull” fluctuating sound – quite unnerving. If I was to explain it in layman’s terms, I would say it seems like the engine wants to change gear, but is unable to. Also, when driving at this “fluctuating speed”, there is very slow response (or none) when I step on the accelerator: If I move my foot down slowly there is little to no difference in power. I need to step all the way down to force more speed and/or the kick down. At other speeds there is no problem. Again, in layman’s terms: the engine seems like it is “in-between jobs” and the revs are not fast to give power when needed (they are not ready for action). When I drive off from a standing position, the car flies and is very responsive. One of the reasons for buying this car was because of its responsiveness – but the problem described above makes it feel as if the accelerator is a wet sponge.
The car’s rpm when idling is stable
I have recently had the air-filter changed: no difference. I had the car taken to the BMW mechanic’s, where, along with other checks, a full diagnostic programme was carried out. This showed no problems whatsoever with the engine – everything is, according to the diagnostics computer, in very good working order. There was talk of the (please excuse me if I get the name of this wrong) “air mass gauge” being defect, but I saw with my own eyes on the diagnostics computer that this was stable and in good working order. The mechanic mentioned something about the possibility of  the actual accelerator pedal having a fault – but admitted that this was pure guess-work.  
So, there it is. I really do hope that there is help out there – I do not want to have to sell my pride and joy because of a fault nobody can find.
Thanks a lot. looking forward to your suggestions.