The Aztec is noisy, so get a good headset, even an active noise reduction one.
Learn to use the hand pump for the gear.
Aztec in training mode (2 people and full fuel) is about a 1000lbs below MTOW, so generally to get it to climb SE should not be a problem.
Be very familiar with the fuel system, to a new ME student it will be confusing.
As in most twins (except the Seminole) VMC is above stall speed so use only half power to recover from the stall as you clean up the airplane.
Do NOT use full power for power on stalls.
Be very careful with VMC demo's (as above), below blueline is automatic intervention.
Fly 17" MAP and 2300 RPM in the practice area, that will give you appr. man. speed. As fell as decent fuel burn.
Engine instruments are generally on the right side, so in front of you, watch them like a hawk and learn to recognize what is normal for your airplane.
Have respect for the airplane, the one i flew was from 1966, so that spar is 40 years old.
Beware of fuel leaks.
BTW, I have tremendously enjoyed my 600 hrs dual given in the Aztec.