Yep been there done that
Almost certainly a duff Maf sensor I bet the fuel consumption is awful
as well and you have to rev the nuts off it at a roundabout to pull away.

This seems to effect every BMW/VW/Merc diesel lump including the 530d

Simply unplug it and go for a drive
Take the engine top cover off it is the thing behind the oil filler in
the air intake pipe going down to the turbo.

The car should immediately be lots lots better
I have a Rover 75 with the same engine
Drove it to Farnborough and back (400 miles) with it unplugged and got
51MPG!

New sensor £150-200 at a dealer Ebay up to £120 but be warned duff ones
still look brand new

If it is the sensor don't change the entire housing which is what you
will end up buying as the lower screw is a pig to get to all you need to
do is undo the two security screws holding the actual sensor in the
housing and change just that, much easier

Does it have an after market oiled air filter if so get rid of it as the
oil droplets can destroy the sensor

On Rovers fine water spray has been known to get past the air filter and
cause failures

These sensors are notorious for failing just about anything seems to
wreck them dust flies anything mine had a spider on it.

Some people say they can be cleaned but I wouldn't bother as you have no
real way of telling if it is working properly.

Ron (link below) sells an amplifier to boost failing sensors, but mine I
think was totally dead.

They are made by Bosch, they have not so far had the decency to offer
low cost replacements, mine lasted 30000 miles only

VW however admit they fail and offer an exchange price but BMW and Rover
still prefer to rip people off, they are so unreliable that I have even
seen suggestion that they should be service items

They degrade over time so you don't really notice the loss of
performance and higher fuel consumption initially.

many people get their cars chipped and effectively only recover the
performance lost by the duff sensor

a good site for info is http://45zs.info/75Zt/R75a.htm

Rover bias but this guy knows his stuff the Pierberg MAF will fit your
car and is a lot cheaper.

Re Window pass :-)