Pistachios and peanuts are not considered to be toxic, but all nuts contain fats, which can cause gastrointestinal upset, including vomiting and diarrhea. Foods with high fat content can also produce an inflammatory condition of the pancreas known as pancreatitis. Many commercial nuts are heavily salted, which poses a risk for the development of sodium ion toxicosis in large quantities.
The bottom line? An occasional peanut or pistachio is not likely to be a problem for your pet, but we wouldn’t recommend feeding him a significant amount of nuts.