For the secondary air system, what starts causing the problems are these things:
- sticky air valve. p/n 11727540471. In time it gets clogged with carbon deposits combined with condensation, and the internal valve gets sticky. One "could" clean it (after it's removed) with brake cleaner or similar, but the best way is to change that part. You will need also a new gasket p/n 11727505259. The gasket is like a "sandwich" with 3 layers. Part of the old one might stick to the engine block when removed.
- sticky "salmon" relay p/n 12631742690 - this could lead to the SAP to stick in the "on" position and fry the pump (expensive to replace).
Usually these 2 items "should" be changed every 80 k miles to avoid those annoying SAP codes, or worse an expensive SAP replacement.
I did this on my e39 couple years back and it's very easy to do.