How can I be sure that the public park uses safe playground equipment?
You can have a look your self, but if you still have doubts the best suggestion would be to go to the local government parks and recreation professionals to inquire about the playground equipment and materials of that playground. Many cities have plans to demolish and rebuild certain playgrounds to make them safer—they just have not done it yet. And many have already replaced every troublesome playground in the city already. So check into it.