In season2, episode5, the beginning of the episode acts like the dog will die, though later it is revealed to be safe. However the beginning may cause distress while watching, even if you know how it turns out.
He's in a hospital waiting room and starts coughing. Goes on for a bit. Once he runs for the bathroom. Look away for visual. He's done but it's visibly there. Forward until 27:45. Note that during the scene a parasite moves visibly under the skin-an indicator as to the stage of the illness
In S03E07 A Dragon-like Dinosaur called “Dracorex” comes through an anomaly into medieval England (likely 15-16th century) where it is injured by a medieval knight who pursues it through another anomaly into the 21st century and attempts to kill it, the Dracorex is saved and healed.