,I do a lot of Multi engine ratings in several types of airplanes from several schools. It's amazing how differently things get taught between different schools using the same airplane. As I posted in the Commercial Single Engine earlier, I encourage everyone to review the appropriate ACS and the Airplane Flying Handbook.
I also encourage everyone to use and follow the emergency procedures as described in the airplane POH. I have seen several applicants deviate from the check list and unfortunately screw things up to the point that the airplane is no longer in their control. Even a few applicants have failed to use the checklist other than for the run up. Using the checklist is a part of good Airmanship.
Here's one situation that continually creeps up on multi engine rides. The applicant straight and level at 5000 feet when an engine fails. As they go threw the engine out drill they let the altitude and or heading drift outside of ACS tolerances. The applicant is so focused on the engine failure that they for get to fly the airplane. So hold heading and altitude while you do the engine out drill. If you are above the single engine service ceiling, hold altitude until the airplane slows down to Vyse and then allow it to drift down at Vyse.
Another problem area is shooting the engine out instrument approach. I usually ask what speed and configuration you will fly this approach at. Unfortunately, most fail to fly what they tell me they will. The biggest issue is they are usually 20 to 30 kts too fast. The second issue is they fail to maintain vertical and lateral guidance within ACS requirements. I recommend developing a profile that uses minimum work load to fly a stabilized approach at Vyse+10 kts (no slower than Vyse) with the gear down and no more than 10-15 degrees of flap.
Last piece of advice....Above all else.....Fly the Airplane!