I have the exact same issue with my 2014 CX-5 Touring and both Mazda customer service and my dealer decline ownership of the problem. Although the 2013 model have already issued a TSB (Bulletin No: 09-002/13) they act like it's tottaly new from them. To make the matter worst, C.S. stated that "The dealership technician determined that your vehicle was operating within the manufacture specifications and operated similarly to other same year and model vehicles from their inventory." so...it's final...it was design to shake. In TSB it's stated that the problem it's caused by "wind pressure" and the fix is fix is "new reinforcement onto the side impact bar-lower and door panel to increase rigidity of the door panel where the power door mirror is located". We will see how soon this will be corrected for the model year 2014.
Thanks.