Physical Danger
In A League of Their Own, when Tom Hanks said, "There's no crying in baseball," he probably wasn't thinking about taking a nearly ninety-nine mph ball right in the crown jewels. Youch.
Don't look surprised―there are small round projectiles heading towards you hundreds of times per game. Every once in a while, a wild pitch or errant foul (or even loosely-held bat) will go flying towards you in an attempt to make a sports show blooper reel.
So why don't we see daily news about another umpire going down in the third inning? Because most of the time, umpires are relatively safe on the field. Home plate umpires are required to wear padding and a mask to protect their handsome faces from spiteful, stray baseballs that might otherwise turn their noses from "outies" to "innies."
Is it possible to maybe get a little hurt? Sure. A coach or player might lose their temper and take a swing at you. You might get beaned by a ball. You could even trip and fall down. However, most of the danger you'll face comes from all that standing still in one position, which can lead to a lot of sore muscles. At least the catcher will probably let you bum some muscle relaxant.