Swapping the MAF might help. I had some harsh shifting and a pretty bad idle (sometimes the engine would stall) when I first got my 2000 540i touring. I bought a brand new Bosch MAF and that solved the issue completely. Nobody ever replaces the MAF so they do start acting up with age and mileage.

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2003 X5 4.6 | 2000 540i Touring

Formerly owned:
2004 Range Rover | 2000 M5 | 2000 540i/6
1995 750il | 2003 Mercedes S500 | 2003 540i/6