I have around 60 hrs teaching for the Multi Rating out of a total of around 2500 hrs instructing for all the licenses ratings and aerobatic and formation instruction as well. Personally pretty much all the really scary moments were doing the ME rating including
1) the student retracting the gear instead of the flaps on a touch and go
2) ending up inverted after the student stalled the airplane during a engine failure during the go around exercise
3) having the student almost feather both engines on short final when they got the knobs mixed up and pulled the props all the way back instead of the throttles.
For most students doing the ME rating will be coming pretty much straight from a C172 or Pa28. They will have little to no experience with retractable gear, constant speed props and faster approach speeds. It is easy to overload the student so you have to take the training slowly and methodically and watch them like a hawk. Things can go bad fast particularly single engine, so if the situation is deteriorating don't try to explain, take control.
Give yourself lots of room. The single engine maneuvers should be practiced at 3000 ft AGL or higher,
For the VMC demo I block the rudder pedals with my foot so the student can only apply half travel. This ensures the VMC roll off occurs at a higher and thus safer speed.
After wrecking one airplane I don't do touch and go landings. All ME training landings are to a full stop with a taxi back and the pretakeoff checklist completed. Also after touchdown I do not let the student touch any switch or control until the aircraft is off the runway.
Bottom line: Watch them like a hawk !