The most dangerous moment with a window air conditioner is pulling it out of the window, because it is heavy and there is a drop below it. Have a helper, support the weight, and then keep the unit upright to protect the sealed refrigerant system.
Pro tip: Let the unit sit and dry for a day before storage so no water sits against the coils and grows mildew.
Watch out: Removing it from the window is the risky part. Support the weight and never let it tip outward, since a dropped unit can injure someone below.