If its a private sale then your buggered.... Sold as seen.
With regards to my comment re exhaust deposits, I need to clarify. Your car should not be doing that. Our Coupe S, does chuck out a bit of condensation from cold andalong with the crap in the exhaust it will drop a tiny amount of crap out of the exhaust. This is also due to the fact that it has a de-resticted centre pipe with is a straight through item.
I think whoever you bought the car from was a little bit too enthusiastic with a hosepipe and water is in the rear section of the exhaust.
With regards to the code, it may be a boost issue such as a split boost pipe or intercooler. Personally I would take it to a garage that knows MINIS and this particular engine. Do you know if the engine has had the timming chains and tensioners replaced? They suffer from "death rattle". At best its a £300 ish to sort the items out, worst case scenario, say goodbye to your engine . Is it nice and quiet from cold?