We're pretty new at this but my number 1 is kids running ammuck. I think that parents that bring their kids to the show NEED to teach them how to behave around large animals. Running, screaming, throwing things, and ducking under the horses belly or neck (saw that this weekend) is NOT the horse owner's issue, but who will get blamed when their kid gets hurt by a horse in these situations?
My number 2 is people (particularly kids) riding around the cars. I know that at many shows part of the parking lot is the holding area. Fine, be in the saddle there, but not riding between cars, jogging and loping up and down the driveway, etc. It's dangerous for the rider and the horse.
These are things that are dangerous and that's what bothers me. If an adult doesn't want to have a connection, or take care of themself, that's their own business, but their kids should be taught how to be safe around horses, both in the saddle and on the ground.