Physical Danger
Needless to say, working with complex machinery and electrical components is always somewhat dangerous. Elevators are certainly no exception.
We've all heard the horror stories about people being killed by a malfunctioning elevator. And unfortunately, no, they're not all the stuff of urban legend (though they are the stuff of some cheesy horror films). So, your safety plan needs to be as on-point as your maintenance schedule.
How do you stay safe? Train early and often on safety procedures. There are people in various sectors, including elevator safety, whose entire career revolves around looking at potential safety issues, then teaching workers to recognize and change unsafe practices. Definitely pay attention to those people.
Most importantly, take your time. The silliest (and often costliest) mistakes always come from rushing through whatever task is at hand. The easiest way to ensure your safety and the safety of those around you is to take a deep breath, slow down, and be as methodical as possible. You're the expert here and you should know what you're doing.
Oh, and watch out for any wacky co-workers who like to prank the new guy or gal. If someone asks you to hold two wires together while he connects them, just ignore him.