When choosing a cooking oil, the ones that have higher concentrations of saturated and monounsaturated fat are best. These fats are less likely than polyunsaturated fats to oxidize when exposed to heat or light.
The Fat Content of Peanut Oil
Peanut oil has a fair amount of monounsaturated fat, but it is also very high in polyunsaturated fat and relatively devoid of saturated fats. This makes it an unstable fat to cook with, and as such, should be avoided.
Mark Sisson has a whole post in which he gives the pros and cons of various cooking oils.