Mihoshi gained her position in the Galaxy Police because her grandfather is the Grand Marshall,because of this fact Mihoshi get's special treatment from her superiors. Also, to keep Mihoshi out of trouble they stationed her in a remote Solar System in the Galaxy, but that's where Tenchi is. Her spaceship Yukinojo is a prototype developed as an error proof system, and if there was anyone that can test that to it's full limits it would be Mihoshi(if it can survive Mihoshi, it can pretty much survive anyone). This ship also has the ability to evolve itself so it can look different from episode to episode.

When she graduated from the Galaxy Police Academy she was partnered with an ambitious young officer name, Kiyone. Mihoshi idlolizes Kiyone and wants nothing more than to spend time with her. But because Kiyone is partnered with Mihoshi, her career has gone nowhere. Almost everything Mihoshi does seems to make Kiyone extremely angry(except for when Kiyone heard that Mihoshi died^_^).

Here's a little math for you: Mihoshi+Washu+Experiment=Disaster. If you ever see this you know there's gonna be some sort of explosion, with Washu yelling at Mihoshi afterwards. Even though Washu sets up security to keep people from bothering her while she is conducting experiments, Mihoshi seems to be able to find her at will. An example of this was when she was finishing her Mecha-Washu experiment and showing it to Tenchi, out of nowhere Mihoshi appears to the suprise of Washu. If you don't know what happened to that experiment I'm sure you can guess. All in all without Mihoshi, Tenchi Muyo! would only be half as funny^_^.