Physical Danger
Being a rare book dealer is super dangerous...if you're allergic to paper cuts. But let's be honest, here: if you became a rare book dealer knowing you're deathly allergic to paper cuts, we can't be held responsible for the consequences.
There's also the possibility that you might become involved in some Da Vinci Code-like plot in which a sinister, ancient brotherhood is out to get your secret copy of the Gutenberg Bible. We'd suggest heading for the back door if Tom Hanks ever enters your shop. He's bound to be bringing trouble with him.
Okay, this has been our snarky way of saying...no, there's not much physical danger in being a rare book dealer. Just make sure you lift with your knees when you're hefting boxes of books, and you'll be fine.