One problem related to oil pump has been reported for the 2014 Mini Cooper. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2014 Mini Cooper based on all problems reported for the 2014 Cooper.
Driving on the freeway, car lost oil pressure suddenly, oil poured out of vehicle, smoking as warning lights indicated "drive train malfunction" and then, "loss of oil pressure: stop vehicle". Diagnosed as a failure of a welding on the oil pump housing. Mini replaced part and returned car to me. Within 1 mile, "drive train malfunction" ignited again. A week later, they reported that there were metal shavings in the oil and the engine needed to be replace. I sold it back to Mini as a lemon.