What are the most common symptoms of hyperthyroidism?

Multiple organs... The thyroid hormones secreted by the gland affects almost every system, including basal metabolism, skin, heart, brain, bowel. The thyroid gland is controlled by a part of the pituitary/hypothalamus gland in the brain in a feedback mechanism (as with all glands). Increased thyroid hormone can be associated with 'poppy' eyes, racy pulse, moist skin, perspiring, diarrhea. See prior answer.
Most common. The most common symptoms are fatigue, difficulty sleeping, irritability or nervousness, increased sensitivity to heat, & sometimes fast or irregular heart rhythm. Other symptoms may include hand tremors, muscle weakness, shortness of breath, increased appetite, hair loss, diarrhea, & change in vision or eyes.