I miss the multi instruction, did 300 odd hours of 6 hour courses (or a bit more on average) 20 years ago but now the average school can't afford to run a twin in the UK anymore, yet they can be cheaper than singles to buy.
I think pilots become more professional having done multi engine.
Don't skip the takeoff brief regards eng. fail proc.
Don't do rushed takeoffs, let everything settle then power up on brakes. (ATC can you take an immediate, reply Negative).
Just watch which mags student switches off when running a dead engine, eg Seneca, can be hard to see whats's going on.
Some checklists are dreadful, write your own if you have to.
Never do touch and go off a sim. asymmetric approach. I saw the result of this, someone cartwheeled and rolled over a Duchess doing this.
Know the flap system, some flaps take a long time to retract to max lift position when doing touch and goes (Cessna 340), could run out of runway.
Also any draggy undercarriages, i think the 337 has a reversed sequence of drag retraction.
Careful complex types like 421, i think someone ruined an engine doing a practise shutdown and start not following correct proc.. Something to do with balance shafts i think.
Don't shut down that engine which you found a bugger to start on the ground, seen that one return for a real asy. landing.
Always make sure the heater works in winter, they can be very cold aircraft otherwise. Make sure the windshield is nicely polished if you know rain is about.
Also could be the first time the student has seen an autopilot if fitted. Engaging that with the roll knob twisted to max can be interesting.