[CaptainCrunch]

I wonder how temporal law would work in the Federation in the future.

I mean just because he killed people in the loop and then kept re-running the loop where they're alive again and he doesn't murder them, shouldn't really be a defense.

I'm sure that when they enacted their final "Con" on Mudd, they said to Lorca that dude he's murdered you about 80 times, killed countless other crewmembers, and yeah they came back but he still actually murdered people. And because they've really established multiple time lines in Trek, especially with the first nutrek movie, in those time lines that he traveled to to different effects, the Captain Lorca's and Tylers would remain pretty much dead and the future changed completely, which means that there are a bunch of temporal laws that were broken.

On top of that just his act of setting foot on the bridge would be an act of piracy and at the very least treason against the Federation. When they took back computer control, they should have seized him because he lost the time Crystal and simply transported him back to earth or the nearest Star Fleet base so that he could face changes and been put away forever. The Captain could also convene a special Court Marshal on his ship, and pretty much shove him out of an airlock since the Federation was "at a time of war" and Mudd was trying to sell technology to the Klingons.