I just changed the oil on my 2006 R53. It has about 105k on the clock.

After completing the oil change, I followed instructions to reset the oil-change count that flashes when I turn on the ignition. The new oil change number is now up to 15,000, but it also says "inspection" each time I turn on the key.

Is that normal? Does that just mean the car wants me to do an inspection the next time I am due for an oil change? I try to reset again to delete the inspection message but now I can't reset it.

 

Yes. It alternates between inspection and oil change. Inspection includes oil change. Take a look in the service booklet. If you don't have it, do a search for mini service schedule.