Physical Danger
Do stress-induced heart attacks count?
The physical dangers of film producing are much lower than kickboxing or underwater demolitions. In fact, they're much lower than even bird-watching.
On a list of "safest jobs," producing probably ranks at least as high as "the guy who writes the safest jobs list." There aren't really any major on-the-job dangers that should concern you. Barring any freak accidents with wild tigers escaping on set or low-flying aircraft, you probably won't need to beef up your "accidental death and dismemberment" insurance policy much.