Hello Matthew,

The exhaust flap should remain closed at idle and open above 2500rpm when driven.
Constant vacuum is supplied to the exhaust flap solenoid in the boot which has a permanent +ve from fuse F3 (ign on). Above 2500rpm the solenoid gets a -ve supply from the engine ECU.
So at idle the ECU supplies no earth to the solenoid allowing vacuum to go through it directly to the exhaust flap closing it for quietness.
Above 2500rpm the ECU supplies -ve changing the solenoid position so that vacuum no longer goes to the exhaust flap and it springs open (for performance).
I think this is a common fault and I first noticed it on my wife's '02 E46 330i when it sounded a bit throaty on start-up. Investigation showed a permanent -ve supply from the ECU (not switching). I wasn't about to fit a new ECU so the solution? I wired in my own -ve supply to the solenoid through a rocker switch under the dash. Now when the wife drives it, it's quiet! When I drive it,I switch it over and it sounds a bit more sporty! - perfect, I don't know why BMW didn't do that in the first place!
It's clearly marked in the wiring diagram for E46 323i and 328i (same thing) in my Autodata Engine Management Systems book 9, page 122, item Y141 - should be in other Autodata diagrams.
If you type E46 exhaust flap into Google images, ther's a great picture and short description (bit small) about third row down.
Hope this helps you.

Colin