My 2011 mini cooper s with 70k idles rough, no check engine. It has a k&n cold air intake (properly installed) and idles rough randomly, mostly when i first start it in the morning. I had the dipstick out and when i put it back in it almost stalled out then it stopped high idleing and went to normal idle, still somewhat rough. I have a video of it idling rough, i can email it to you if you want to see it since im on mobile. Thanks.

 

I am having the same problem but I have n14 you might check inlet pipe, spark plugs