Law and Order in Star Trek

First contact episodes of Star Trek give us an interesting look at the law both in and outside of the Federation. Let’s take a look at a few of the more unique legal systems encountered by Enterprise crews!
Argrathl
Instead of incarceration those sentenced to prison for serious crimes on Argrathl are actually implanted with the memories of being in prison in a process that takes just a few hours.
In DS9’s 19th episode of the 4th season “Hard time” written by Daniel Keys Moran and Lynn Barker, Chief O’Brian is trialed and convicted of espionage for asking too much questions. Throughout the episode we’re following his prison time, just to find out it is just an implanted memory, but still so real and vivid for Miles it interfere with his life for a long time after.
Banea
Baneans, similar to Argrathl use implanted memory, but this time a memory of the victim at the point of death and the memory is set to be relived continuously.
In Voyager’s episode 8 of the season 1 “Ex Post Facto” written by Michael Piller and Evan Carlos Somers, Tom Paris is accused and convicted of the murder of the scientist Tolen Ren and is implanted with false memory of him killing the scientist,  what is later revealed in investigation lead by Tuvok.
Edo
Edo have no police or law enforcement but mediators who select only one area each day as the punishment zone. Since it’s a completely random selection, no one knows when or where a zone will be and so no one risks death.
In TNG episode 8 of the season 1 “Justice” written by Worley Thorne and John D. F. Black Enterprise stops at the newly discovered planet Rubicun III. Its inhabitants, The Edo, live in virtual utopia. There is almost absolutely no crime on the planet.
After Wesley Crusher accidentally fall into the greenhouse he is explained that all the crimes are punished by death.
Ferengi
Their culture and legal system is based on economy and “Rules of Acquisition”, sacred code on which all of Ferengi society is based.
In DS9s 23rd episode of the season 3, written by Ira Steven Behr and Robert Hewitt Wolfe, an agent named Brunt serves Quark with a Writ of Accountability for improper supervision of a family member. Ferengi law strictly forbids women from earning profit, leaving the homeworld and wearing clothes. Quark and Rom’s mother, Ishka did it and Quark as oldest mail is responsible and he has to return to Ferenginar and convince Ishka to confess, as required by Ferengi law.
In DS9s 25th episode of the season 4, written by Louis P. DeSantis and Robert J. Bolivar “Body Parts” presents Ferengi supremacy of contract, as in “a contract is a contract is a contract.” This applies, per the 17th Rule of Acquisition, only for the contracts between Ferengies.  Quark in this episode during the physical finds out he’s going to die soon of the rare disease and to pay off his debts he is selling his vacuum-desiccated remains on the Ferengi Futures Exchange. When later finds out his physical was in error he wants to break a contract, but Brunt, the buyer warns him he’ll be stripped of his license to conduct business within the Ferengi Alliance.
Mari
Mary, who accomplished virtually crime-free society, by completely purging themselves of violent thoughts consider even accidentally projected violent thoughts a crime and it is sentenced by punishment of an engramatic purge.
In the Voyager’s episode 10 of season 4, “Random Thoughts” written by Kenneth Biller, someone bumps into B’Elanna irritating her,  she calms shrugging it off as an accident, but later that thought was encountered few times, even causing death. Since she was deemed aggressor she was sentenced to undergo memory modification to remove the thought.
Trying to save B’Elanna, Tuvok follows the trail and finds existence of underground trade in violent thoughts.