Final answer:
The most important parameter for the nurse to assess after initiation of mechanical ventilation is the oxygen alarm on the ventilator.
Step-by-step explanation:
After the initiation of mechanical ventilation, the most important parameter for the nurse to assess is the oxygen alarm on the ventilator. This parameter indicates the functioning of the ventilator and the delivery of oxygen to the patient. If the oxygen alarm is not functioning properly or if the oxygen level is low, it could lead to further respiratory distress and compromise the patient's oxygenation.