Physical Danger
Well, the good news is you're not attempting death-defying stunts or being chomped to bits by an alligator. You're not safe from danger, though—not by a long shot.
First, consider the materials you'll be working with. Kilns are insanely hot, and they can make poorly-made pottery explode. It's not like a big, epic explosion from a James Bond movie, but when you're working with a hot machine that might make your work go boom, you should exercise caution.
You'll also be working with some pretty toxic stuff, unless you're going a super-nontraditional route and using glazes made of, like, corn or something. Traditional glazes are full of silica, which is quite toxic. Most clays have a high silica content, too, which means that pottery studios are chock full of silica-heavy dust. It's not enough to kill you, but it can do some damage to your lungs over the course of a few decades.
Finally—yes, there's more—you'll undergo a fair bit of wear and tear just from your daily routine. Whether you're pinching pots or throwing them, you're likely to be hunched over your work, making small, repetitive motions with one hand but not the other. That kind of repetitive, asymmetrical strain is really hard on your back and the joints in your hands, especially if you do it every day. You can lessen the strain a bit by using soft clays...and taking breaks.