Primary symptoms include headaches, fatigue, loss of appetite, weakness, dizziness, light headedness, insomnia, nausea, shortness of breath, nosebleed, drowsiness, swelling and diarrhea.
More serious symptoms that may indicate life-threatening altitude sickness may be due to Pulmonary edema, which is fluid build up in the lungs, which would have symptoms similar to bronchitis, dry cough, fatigue, and difficult breathing. Cerebral edema, which is the swelling of the brain, would have symptoms including serious headaches, unsteady gait, increased nausea, vomiting, coughing blood, loss of consciousness, and even coma.  
Unsteady gait is an early and primary indicator that someone is suffering from serious altitude sickness.