Physical Danger
The general danger of driving an automobile is in full effect, which is mild if you're at least half competent (please be at least half competent). However, chauffeurs are also responsible for the well-being of their clients.
If something happens to you, it's likely going to happen to them―only worse, because they're probably not wearing seat belts and don't have any airbags back there. Keep them safe by keeping yourself safe, and prevent your back seat from becoming a spinning fun house of horror.
Another thing to keep in mind―and you'll learn this fairly early in your career―is that many of your clients will have been drinking/will continue to drink at some point before and/or during your interaction with them. This may cause them to make what scientists refer to as "stupid decisions."
You never know when a friendly disagreement about college football team preference will turn into an all-out brawl in the back of your car. Always be aware of the condition your clients are in—the life you save may be your own.