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Peanuts are non-toxic for dogs, so it's okay for them to eat them. The only time there's a concern about a dog eating peanuts would be if the nuts were moldy...then the dog would show neurologic symptoms such as staggering, seizures, ect.
Most nuts are perfectly fine for dogs to eat in small amounts. The only one we really worry about would macadamia nuts.
I hope this helps.