The long term trim (block learn) is the one that matters, it's normal for the short term trim (integrator) to go up and down, if it can't keep up then it bumps the long term a notch and tries again. The o2 sensor should be cycling so that is good but if that is different after changing the MAF then you gotta wonder. The only way to really rule out the MAF is to replace it with a known good one. Puma is right about resetting the adaptations but in cases like this you can also just watch to see what changes starting from where you left off instead of re-setting and starting over. Also triple check the MAF connector as has been pointed out, they get yanked on a lot so you might have something going on there.

AND as has been pointed out CHECK FOR VACUUM/AIR LEAKS.

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)