When the American Revolution was covered in High School and College, there seemed to be a bit of a narrative that King George was mad (or at least unreasonable) and that this was a factor in the escalation into what became the American Revolution. So, was he truly mad? Could a more level-headed king have resolved the situation peaceably?
George III suffered from porphyria, a genetic condition that left the kidneys unable to process toxins in the blood properly. This lead to occasional bouts of madness (also, his urine turned blue!). However, there is no reason to believe that the King's condition affected Britain's American policy. The disease did not fully manifest itself until 1788, and the even then the King wasn't the one handling the day-to-day running of the government anyway. These policies were largely devised and administered by Parliament (which, was, admittedly, run by a government formed with the king's consent). The ineptitude of Lords Germain and North have a lot more to do with provoking the American Revolution than occasional oddness on the part of the king.