Power
When the word "justice" is in your job description, you can go ahead and assume you'll be wielding some power. The question is: just how much? Even though you'll be dealing verdicts a-plenty, they'll mostly be for those looking to escape a parking ticket or a citation from a night of disorderly conduct.
Keep in mind that you're serving at the lowest level of the court. Not only does this mean your decisions are made on a smaller scale, but they can also be appealed and brought before judges with greater power who are able to reverse your decisions.
Power is in the eye of the beholder, really. Few of us out there in the world are capable of the kind of power allowed in this field, so it's nothing to be taken lightly. No matter how small the cases may be, justices of the peace are still making decisions that impact society. Hold that gavel with authority, my friend.