Although not strictly shutting down the wrong engine, there was a close shave with a Dakota after the instructor reached across and caged the artificial horizon as the gear was retracting after take off. It was an instrument rating test and the take off was "under the hood".
Coincidental, and a classic example of Murphy's Law, the aircraft yawed and rolled sharply to starboard as the AH was caged. The pilot under the hood could see the instructor had not touched the throttle or mixture levers and so he called "engine failure No 2" and attempted to press the relevant feather button.
The instructor managed to stop the button from being actuated as there was no indications on the engine instruments that an engine had packed up. A quick glance outside revealed the rubber de-icing boot on the leading edge of the starboard wing had split asunder throughout its full length leading to a fairly dramatic loss of lift on that wing. The aircraft was landed safely after a circuit requiring full aileron and some rudder.
During the war there were several fatal accidents to Lancasters where following the failure of one engine, all four engines (props) feathered simultaneously with the actuation of one feathering button. One of these instances (fortunately non-fatal) was described in the book by Norman Mitchell called "Flight of the Halifax". Mitchell was a ferry pilot and lost all four engines in flight during a ferry flight after conducting a test feathering of one engine. A similar story emerged when the Australian magazine The Bulletin interviewed a former Australian bomb-aimer who managed to bale out at low level when all four engines feathered after the flight engineer had attempted to feather one engine that had lost power.
I personally experienced the same phenomenum while conducting an engine run up on a Lincoln bomber on the ground. On the pressing of one feathering button, the other three engines all feathered. The defect was traced to a short circuit in the metal cage surrounding the feathering buttons and the metal dimmer switch incorporated in each button. Where under certain circumstances the dimmer switch of any button touched the protective cage while that engine was being feathered, it sent a current to all the other buttons to feather the prop.