I'm in the same boat as most it seems. I have tried Shell V-Power, BP Ultimate, Total Premium and Tesco Momentum, none seem to make a difference to this issue, but it didn't like the Tesco Momentum stuff when starting so in my experience would steer away from that (but it's so cheap

).
Video of mine, the dips seem a little bigger than the OP's, when hitting 500rpm the lights in the car dip a little, that's how close it is to stalling. Drivers door is open and I'm in a garage so you can hear the "pop" or "misfire" sound when I tip in. I'm really pressing the throttle down far and quickly, quite an aggressive tip in. If I just roll on to the throttle a bit slower there are no "pop" sounds and the engine picks up cleanly.
[youtube]m2YaQZHILR8[/youtube]
My ideas so far much along the lines of most, ECU clearly doesn't know how much fuel or air is going through the engine at the time, so MAF or front lambda sensors. Would start with the lambda sensors (I will get round to this myself when I get some time...).
As for the M3 not suffering with this, I think I read somewhere that the Z4M uses a different ECU, something more closely related to the V8 M3 and the V10 M5. This means they would have carried over the calibration as much as possible, but there will be some significant differences I'd imagine. **EDIT** Bit of reading and can confirm the S54 in the Z4M uses the MSS70 ECU and the MSS45 ECU is used in the E46, could explain some difference at least.
Also, don't know if this is only in my head, but it seems to be worse when it has been raining (which is always in the UK :| ), so it might be something to do with the humidity correction in the calibration not quite being right for the Z4 induction system.
Be really interested to know how others get on
