Ok, so here goes.
The first thing is to be very on top of your speed. If you let it get away from you then you either won't be landing on that pass or you will discover what happens when you touch your brakes with very little weight on the wheels. Sliding off the runway when your wheels lock is a very real possibility.
On take off make sure you get the gear up before you pass 80, otherwise it takes a lot more effort to get the gear up. It will take a while to get the hang of bringing the gear up from the right seat but once you get it down it's very easy. At this point you will learn what they mean by the "Mooney wave" on your climb out. The manual gear is great since it's almost fail safe but I recommend you don't do touch and goes. There is just way too much room for error. Finally with take off make sure and brief the PAX that for no reason what so ever should anything be placed between the seats since that will block the catch on the floor and keep the gear from locking up. That is no fun.
On landing two things: full flaps or NO flaps, do not use a partial flap setting because you just won't do anything but float. The next thing is trim. With full flaps, 15", and full nose up in a properly rigged aircraft you will get a nice easy plane to land. On some models, especially the ones with the 201 cowl mod, you will get a great deal of backfiring on landing. At the low power setting it will sound like a muffled "popopopop" but it can be cured by leaning the mixture out slightly. Once you're on the ground get the flaps up before you touch the brakes, see above. Once you're stopped and about to get out...RESET THE TRIM! I've seen more than one nice Mooney end up as a ball because some got rushed, excited, or just plain stupid on the next takeoff and forget about the trim. It doesn't end well.
Dropping the gear can be hairy if you put your hand in the wrong spot at the wrong time. Trim can be your friend here too. Start slowing the plane down and make sure that you don't drop the gear above 120. If you do you will run risk of cracking the gear doors on their leading edge abeam their attachment points about halfway down the door. Thats a pretty good tell for a bad Mooney driver. If you trim it for 120 and drop the gear that will almost perfectly set you up for 110. Get her down to flap speed and when fully deployed that should give you a nice decent rate and somewhere around 85. Your mileage may vary depending on how well it's rigged.
On preflight there are two really big items to watch out for. First, make sure that the pilot shakes the wings pretty hard for and aft at the tip. Some tanks and bladders have a bad habit of trapping water which doesn't make it to the sumps. Once you make a turn on the ground that water can break loose and find it's way into system on takeoff...That ends badly and I have pictures to prove it. The next thing is to check the fuel selectors for movement and you must feel the detent. They are prone to sticking.
The last thing to do is teach them about flying single pilot. When you're flying a manual gear Mooney solo before you even start the engine make sure to buckle the passenger side seatbelt and sinche it down tight. If not, and this will happen a few times, the unlatched buckle will fall down between the seats and keep you from being able to lock the gear.
I'm sure there is more, but thats all I've got for now.