In fact our medical system is safer then road travel by car, or aircraft. We expect 100%safty, but that can only happen in fiction. Yes, people have lost the wrong limb, or got the wrong blood or the wrong dose of a med. It is unbelievably rare in terms of percentage.
Many of the mistakes that are recorded are harmless non events. A med error happens when a med is given late, in most cases that has zero effect on the person getting the med. it is nothing more then a book keeping mistake. Such mistakes happen because an emergency in another room or just plain poor staffing due to an outbreak of local sickness.
Some mistakes are protocol mistakes. A person should get test or treatment a before b, but due to symptoms the doc or the staff on hand goes directly to b.all and all you are safer in a hospital or with a paramedic in your house then any where else in the world.