Physical Danger
Obviously, this isn't stonemasonry or policing or wrestling or any of those really dangerous careers. This is drama: all of the conflict is fabricated. When Carmen croaks in Act III (uh, spoiler alert), the curtain falls and the actress makes her way to the wings to emerge reborn for a triumphant curtain call.
That isn't to say there aren't some dangers in the opera world. The actual staging of these shows isn't usually the over-the-top showmanship of musical theater on Broadway, but the sets are still big, dynamic, complex, often movable, and occasionally on fire. When a big hunk of plywood is barreling down at you, cut the music and get out of the way.
Knowing your stage left from your stage right (hint: looking at the audience, not from the audience) could save you from bodily harm. There will be a stage crew in charge of moving the set, cuing the curtains, and running all the special effects, so make sure you listen to those people―they're not just shouting because they're paid to.
You've also got to make sure you take care of your instrument. The vocal chords with which you reach the highest heights (both range-wise and to the back of the opera house) are delicate organs. You'll be putting stress on them constantly; this can lead to a whole host of icky nasty issues including inflammation, infection, and gross things. So make sure to treat them well, and please, for the love of Wham!, wake them up before you go-go with a gentle warm-up.