While oysters aren't on the Pet Poison Helpline's list of toxins, it's a wise idea to avoid feeding them to your dog. The oysters may have eaten toxic algae called dinoflagellates, whose toxins concentrate in the oysters' tissues and can cause paralytic shellfish poisoning in both humans and dogs. Because these toxins are not affected by cooking, you shouldn't risk Scruffy's health by feeding him oysters.
You Can't See the Toxins
Oysters are filter feeders who thrive on plankton, including the one-celled dinoflagellate algae. Toxic dinoflagellates are the algaes that cause poisonous red tides. While not all oysters have been exposed to toxic dinoflagellates, you can't tell whether an oyster has a concentration of the toxins -- gonyautoxins and saxitoxins. Even if the oysters didn't make you sick, reactions to the toxins vary according to species, health and weight, and may result in a serious reaction in Scruffy.