I had it on my '04 2.5 and have it on my '06 M. Must be a "USA Thing". You would think they would save the money on cars shipped to the other side of the pond and leave the bracket off.
The Secondary Air Pump is a known problem for failure. Not really that often but more than other parts on the car.
The SAP runs upon engine startup for 90 seconds. It injects air (oxygen) into the exhaust gases to allow any unburnt hydrocarbons to have sufficient oxygen to burn off, and to help the O2 sensors to heat faster. This is due to (as stanley said) the emissions system (O2 sensors) to be running in 'Open Loop' mode and the DME using a default fuel mapping. The system will go into 'CLosed Loop' mode when the O2 sensor heaters reach approximately 600'.
The SAP should NOT start then stop then start again. It should just run for 90 seconds.
You should be able to hear the pump running at startup. Especially with the hood open.
From http://forums.bimmerforums.com/forum/showthread.php?1319763-Secondary-Air-Pump