Pistachio nuts are not toxic to dogs. However, pistachios and many other nontoxic nuts such as peanuts have a very high fat content, which can cause illness if eaten long term in large quantities.
Macadamia nuts are toxic to dogs in and of themselves, but other nuts, including pistachios, present indirect hazards. In addition to causing inflammation of the pancreas due to their high fat content, nuts and nut shells also present a choking hazard and can cause obstruction of the bowels. Salted pistachios can cause salt toxicity if eaten in large quantities without proper hydration ready. Moldy pistachios eaten by an indiscriminate dog can cause seizures or even be fatal.