I don't think this is the problem but I only use OEM oil filters. I know some guys here use Wix. Has there ever been any metal in the oil or has the oil been more reflective then normal? If it is idling at the proper RPM it could be a bad oil pump or your crank bearings are worn out. Both of these would be rare at that milage. Because you can I would check and see if there is any codes.
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Oh yea it could be a bad oil pressure switch. Start simple. number 8
http://www.realoem.com/bmw/enUS/showparts?id=RE33-USA-08-2004-R53-Mini-Cooper_S&diagId=11_3395 -
My oil filter looks more like http://www.realoem.com/bmw/enUS/showparts?id=RE33-USA-08-2004-R53-Mini-Cooper_S&diagId=11_3762 If that matters. No support cage in the middle.
The part is ordered, I'll let you know how it turns out.