The biggest danger is not following labeled directions exactly -- especially when it comes to not using dog products on cats.
Before using a flea or tick product, you may want to ask your veterinarian what works best for your animal.
Here are a few extra tips from Dr. Marty Becker:
You Can Worry a Bit Less About ...
Puppy diseases: Yes, your puppy can pick up diseases from other dogs who are sick. But your puppy also needs to be socialized to grow up relaxed and comfortable. Don't take your puppy anywhere other dogs are (unless they're dogs you KNOW to be healthy and current on vaccinations, such as a friend's dog in a friend's backyard for a playdate) until your vet gives you the go-ahead after the last shot. But DO take your puppy where people are. One great way to meet-and-greet: The patio of a coffee shop. Bring healthy treats for your puppy (water, too!).
Chicken bones: While cooked poultry bones are not safe for pets to eat, they're not instantly deadly, either. Once they're in the system, they'll probably be digested just fine. But do talk to your veterinarian if your pet eats any and take your pet in if you see any sign of illness.
Raw meat and eggs: Dogs aren't as susceptible to salmonella as people are. A healthy dog will probably do fine if exposed to salmonella. But since humans aren't as strong against salmonella, the real problem is what could happen when you handle food with a problem. Kibble and treats have recently been recalled for salmonella. Take precautions with ALL food, even pet food, for your own sake: Wash your hands regularly, and keep food prep areas clean.
... And Worry More About:
Swimming: Not all dogs can swim. Short-faced breeds such as the bulldog usually can't swim and they can drown easily. Even water dogs like Labradors can drown if they get too tired, the current's too strong or the water's too cold. Cats usually do OK. They can swim, usually pretty well, but they sure don't want to. And beware the warnings for algae blooms. If a pond or lake isn't safe for you, it's not safe for your dog.
Cats and string: Yarn, ribbon, thread or even the juice-saturated string from a roast -- your cat may eat any one of these and need surgical intervention to live. The cure is easy: Keep a lid on the garbage and put all hobby projects safely away when you're not working on them.
Temperature extremes: Perhaps because they seem more "wild" then we are, we tend to think pets can handle high or low temperatures better than we do. But not so, especially for pets who are unfit, chronically ill or aged. Always protect pets from cold or heat, using shelter, protective gear and -- for heat -- having lots of cool water available.