Let me be the first to congratulate you on your new prestigious position as Magistrate! I complained enough about it, but it was fun. I can give you what my perspective was, but keep in mind you are going to have to develop the role to fit yourself and your style of play.
The way I saw it: Laura is an outpost at the asshole end of civilization. In a way, it makes you sheriff, judge, and the only keeper of any law and order needed for civilization. The most important thing is to learn as much about the laws of Gor as you can. This is going to give you a frame work, but not everything you need to be effective.
You will be the chief cook and bottle washer of the law, and though it sounds bad on the surface, it allows you the ability to develop consistency. Yes, you can expect problems to the docks to be yours, as well as city, and even occassional non-city players falling under your perview.
In a way you WILL become the IC bitching post, at least as much as you allow. This also isn't a bad thing. As a character, you aren't required to be reasonable and rational. If people are bringing piddling problems to you, react like an important man does, or rather over react like an important man does. Screaming angrily has gotten rid of more time-wasting issues then reason and rational ever did, at least on Gor. Some rumor mongering, tension and conflict is vital to roleplay, don't squash every little bit, let them work out the minor stuff.
Don't let people usurp your authority. You are charged with a responsibility. You catch your own men collaring women of your own Home Stone, well, they have just circumvented your authority. It goes with every enforcement of law, well with a couple of exceptions. I didn't mind when an Outlaw was impaled (One wily warrior used that permissiveness to impale someone who wasn't an outlaw, which was fine, I never found out in character.) You can figure out if you want exceptions or not.
Treat the Warriors with the utmost respect. To me, they were absolutely the greatest asset. By the same token, be able with weapons. You need their respect to be effective. Be strong, when the city is attacked, try to be the first to engage. If there is a localized event, for instance panthers taking a captive to the woods nearby, try to go along with the Warriors in an effort to rescue as an extension of defending your city. Do not go on raids with them as a scribe, though, thats their property, respect that.
Don't shirk away from the duties of a Magistrate. You will have to be the executioner at times, there simply isn't enough people to play that. Make it public. But don't overcomplicate your duties. Gor isn't America, and there is no Miranda Act, they get a trial when... and IF you say they do. Trials are complicated as hell, most times its hard to get 3 people to meet up for roleplay without real life interfering, imagine trying to get legal counsel together and executing a trial with witnesses? Remind them as you lower them on the spear if they wanted an overblown trial they should have tried to collar a free woman in Ar instead.
The Administrator builds the city and you defend it as a city, and not a series of buildings. You are law and order, but don't aim at oppressiveness. People need to get away with things from time to time, or they won't take risks, and that makes for dull roleplay.
I hope you have as much fun as I did with the role. Make it your own. Be available, as much as you can on the weekends, thats when you'll be needed most.
Keep the OOC seperate from the IC, especially when observing evidence. Don't sweat the bad guy getting away sometimes, its Gor, the bad guy is supposed to get away from time to time.