According to the internet, the Florida Dept of Agriculture and Consumer Services inspects all rides at parks that employ fewer than 1,000 people. The large amusement parks have their own specialized full time inspectors. I think there are special rules for the big parks, like they have to have a trained engineer inspector for specific permanent rides, or something similar.
I wonder how this responsibility was given to the Dept of Agriculture, but probably because of all the county fairs, which always have livestock shows and auctions. Then the rides became more important than the farm aspect, and someone had to keep an eye on safety.