Physical Danger
We won't insult you by sugarcoating it: as a police officer, you do have a higher injury risk than employees face on many other jobs. After all, many of the criminals you chase will be uncooperative, and will go to any lengths to get away from the law.
While you're running after them down the sidewalk, you may trip over a stray skateboard and go for the ride of your life. If you're chasing the miscreant in your patrol car, you could run into a garbage truck, street drag race, or yet another red light-runner. Then you've got two lawbreakers to pursue. Finally, you may encounter an injured citizen to whom you must provide first aid.
However, you can minimize your injury risks through proper preparation and practice (say that three times really quickly). Your police academy coursework will likely include suspect apprehension techniques, defensive driving instruction, and the proper use of personal protective gear such as CPR masks and gloves. You'll discuss and role-play many scenarios, and will benefit from your instructors' years of practical knowledge. In short, you can do a lot to stack the deck in your favor.