We had the same problem
My wife's new X3 also succumbed to the whining rear wiper/washer! The car was built during the second week of December. Our dealer old us the parts would take 2 weeks to be shipped from Germany (frustrating given that the car was built in S.C.). We were offered a loaner, but my wife preferred to drive her car. This is our 6th BMW, but I must admit that having a mechanical defect with a brand new car (but a model that has been in production for a while), is making me think about purchasing a 7th (I have been planning on replacing my '08 3 series 'vert when the new model comes out).