Apart from possibly causing a little vomiting or diarrhea, or maybe an obstruction if you have a small dog, there isn't much else to worry about. Squirrels can carry intestinal worms, so I would have your vet prescribe a broad-spectrum dewormer to give your dog to treat anything like that.
Rarely squirrels will carry rabies, so if your dog got bit by the squirrel I would have his rabies vaccination boosted within 48 hours of the bite. Bites can also become infected, so your vet may want to prescribe antibiotics, too.
She's a 30-pound border collie mix, and she seems to be doing OK. I'll get the dewormer when we get back home. No bite marks evident. (I just saw a tail hanging out of her mouth.
Give her a pat on the head--it is a fast dog to catch a squirrel! : )
Thanks so much!