Culprit found!

Secondary air pump line has a crack in it.

http://www.xoutpost.com/bmw-sav-foru...ange-part.html

This maybe a long shot for the E53 but the E60 has a vacuum operated a exhaust valve near the tailpipes that open up under increased vacuum when engine revs over a certain rpms maybe that valve is stuck open OR you forgot to plug in the vacuum hose for it after your repair.
All this is me assuming the E53 has the same setup there as the E60's.
Hope this helps.
I stumbled on this thread as I have intermittent opening of that valve when driving thru heavy rain......??