2010 Cooper S with 73K miles. Just had it at the dealer for a thermostat and they also replaced the air boot between the turbo and airbox. My daughter drove the car very short distances for the next few days and all seemed ok. She was on the freeway for the first time since the repairs and started up a hill - car started to stumble/misfire and the CEL was flashing amber. CEL went out and was out when I got to it. Car now idles rough and the CEL did come on again. Got codes P0300; P0303 and P0304. Called the dealer and the first thing they suggested was bad fuel. I changed the plugs and all four coils. Car was low on fuel anyway so ran it lower and filled with Chevron Premium and added fuel treatment. None of this has helped - same exact symptoms. At highway speeds the car seems normal and has normal power, although at times it will misfire and the CEL will flash under load - other times it's okay so seems intermittent. The misfire / rough idle is evident when idling or at low speeds. Sorry for the long explanation, but any assistance or ideas would be appreciated. Thanks!

 

i will make it very short , I had sam issue : replace fuel system assembly with new fuel pump and replace fuel filter otherwise full fuel filter assembly available in e bay total around 400 USD.
replce spark plugs if you have already changed new spark plug coile

 

Thank you for taking the time to reply. This turned out to be a bit more than I ever would have expected. A chunk was missing from one of the exhaust valves which also caused damage to the piston or cylinder. Dealer replaced the engine. I will say that BMW / Mini is a great company IMHO. Too much to go into here, but they really stepped up on several occasions with this car. I have owned four BMW's and this one Mini. This situation could have turned me off to the brand forever, but they stepped up and the result is an even more loyal customer.