if the vibration damper is also known as a harmonic damper, then my friend, i'm in the same boat!
Basically, had noise (passenger side, under acceleration, (not in neutral). Sounded kind of like a knocking. Searched the mini2 threads for "knocking noise". Good night! A large number of users having same problem. In a nut shell. Took Wedge (My mini) to the dealership, they verified that there was a noise, didn't know what it was. Showed them the posts on mini2 board. They decided to give it a shot by resplacing damper.
Fun part - part came in last week. However, dealership needs five tools to put in on. 3 came in, two are on back order. And no one knows when they will be in! (Not the dealer's fault, they have been extremely professional and courteous/accomidating! = excellent service!) (Jackie Cooper BMW/MINI of Oklahoma City - if your reading this, some mini accessories would be nice!)
Anyway, I feel your pain. Mini's are like high maintenance girl friends!