There are many safeguards against infection. Especially in an environment like a dentist office, where patients are seen by appointment, they stay much more on top of things. There isn't a lot of cause to be worried, especially with such thorough sanitation requirements.
Reusable equipment is placed in a sterilizer where temperatures go so high it kills all bacteria and other organisms. First the instruments are placed in a cleaning solution. They are then placed into special sleeves, sort of like an envelope.....the sleeve is closed and then it is placed into the sterilizer. when it comes out, the sleeve has a special marking on it indicating that the temperature in the sterilizer reached the adequate level to kill all organisms. The instrument is then not opened until it is to be used again. Some of the instruments and tools are disposable, and used only on one patient but most of the tools are sterilized and re-used. Every office has to keep a detailed record of every sterilization. If you are in doubt, ask to see their sterilizer and the sterilization log.
Surgical instruments for major operations are processed in the same fashion.
If a dental office follows the guidelins or protocol of OSHA, catching an infection from routine dental procedures is extremely rare.