Autozone code reader found P1421 & P1423: BMW specific codes
A search of the net finds that these codes indicate low oxygen in both exhaust manifolds. Nothing serious though - the oxygen is delivered by the secondary air pump for about 100 seconds after a cold start - now I know what that thing is that sounds like a vacuum cleaner.
The pump is actually fine and has no signs of corrosion which can be caused by exhaust gases coming back through a defective non-return valve on the manifold.
So I browsed around some more, and found that a relay in the main power distribution box can be bad, giving these codes. Pulled it and re-installed the same one, went to Autozone and had the codes reset.
Codes came back a few weeks later - pump still hums normally during a cold start, so I know it's not a serious problem, but does anyone have an idea what the problem is. Intermittently bad relay is my best guess.
Cheers