Are there any common and identifiable hazards to being a Chemistry Teacher?
I have been teaching chemistry at the college level (if you include my years as a TA in graduate school) since 1999.  While there are certainly dangers involved in dealing with hazardous chemicals, I would not say that the job is unusually dangerous if you follow safe practices and use decent equipment.  I have known many chemistry teachers and professors who lived well into their 80's and beyond.  You're probably going to find certain workplaces which, for whatever reason, are more dangerous than most.  I have heard of (but not verified) an incident at a local college where five female biology professors were diagnosed with uterine cancer, an event which is extremely improbable to occur by chance.  Obviously, there is a substantial need to investigate such a situation and see if there is a common carcinogen present which is causing the cancer.  Such a situation could conceivably occur in the vicinity of a chemistry lab, although it seems unlikely if all standard precautions are followed.

The greatest source of danger is likely to be the students themselves.  When you have many young people together who are (1) easily distracted, (2) not particularly aware of their surroundings, and (3) lacking in manual dexterity (e.g. clumsy), they are far more likely to be a source of injury than the chemicals on their own.  So long as you are willing to invest the time in enforcing safety in your labs on a consistent basis, I think you're going to be just fine.