car looks pretty clean, but definatly get a carfax. the VIN or Vehicle Identification Number is the car's ID and is usually located on the dash near the winshield on the drivers side. CARFAX will give you the vehicles history.
also, i would definatly take the car to a BMW shop and have it fully inspected. its not free, but a car with 350,000 miles is old. i would get it checked out. good luck with your purchase.
also, have you thought about looking at E30's? you could pick one up with much lower mileage for $3200. just a thought.
