After many hours and years of instructing, both flight school and air carrier, I have a few opinions in this area.
First of all, ALL emergencies need to be discussed BEFORE the lesson. It is the only way the student will get the full benifit of the lesson. The instructor does not have to tell the student exactly when it will occur. As an instructor you're not there to trick or surprise the student, but to expand his knowledge.
At least once during primary training the student needs to see the propeller stopped inflight. The dynamics of gliding with the prop stopped is different than when it is windmilling. Right over the airport, uncontrolled prefered. It can be a great confidence builder.
In multi engine aircraft, I always had my students completely shut down an engine at least once. Then when it happens for real, it is not so much of a shock. It's fun to see the look in ths student's face when he/she looks at the visible prop blade. It's not so fun when your co-pilot after seeing the stopped prop for the first time, drops the checklist on a dark and stormy night. And that has happened to me at least once.
When I was instructing at a flight school, pilot controlled lighting was common. I would have my students land without landing lights. And at least once land without runway lights. After a couple of landings with the runway lights. Did this because the flight school had, had a couple of incidents where the student panicked when the runway lights went out during the flare. I was not teaching dopers. After we started doing this, the incident rate for this type of event dropped to zero.
Before I would sign a student off for his/her checkride, I would instruct them in downwind takeoffs and landing. I would discuss the dynamics and the effects. Reason for this there are many one way airports, terrain, noise or local convention being the the reasons. It would get their attention. The amount of runway used changes dramicly. With my instrument students, I would have them shoot approaches and land downwind. Always keep in mind tailwind limitations and/or performance.
Besides the normal covering of gyros. I would cover airspeed indicator or tach. In complex aircraft would cover tach or MP gauges. It is surprising how close the student would come to getting the right setting.
On the second dual cross country, I would tell the student to just consider me a passenger. He/she would do everything on their own. Liked to do this on a hazy day, not much more than 3 miles vis. While enroute I would distract them and get them turned around. Then I would start acting like a panicked passenger. Then I would let them try to figure where they were and how to get to where they were going. Usually they would dig themselves out of the hole. But if they needed help, I would ask them about the VOR, 'What does this do?' or point to the radio and ask 'Can't you call someone?' At this point I would introduce radar vectors or DF steers. This exercise allowed them st see in a controlled setting that they can work their way out of a situation. So if it did happen on their solo cross countries, they were less likely to panick.
I don't like to see pre-flight problems as a contest between instructors. But a problem or two for the student, especially after solo, will keep them sharp. Tape on the pitot tupe or static port. A flat tire or miss tire. Don't be surprised how many miss them. Dual flights only and keep track of them.
I would also mix avgas with jet fuel. A potenial problem. It is not easy to see.
Last piece of advise. Like my old Sargent used to say "Stay alert, Stay alive". It holds true almost everywhere. Be Careful.